Content-Type: multipart/mixed; boundary="-------------0403050341659" This is a multi-part message in MIME format. ---------------0403050341659 Content-Type: text/plain; name="04-63.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="04-63.keywords" polarized vacuum, Bogoliubov-Dirac-Fock model, Hartree-Fock, Dirac-Fock ---------------0403050341659 Content-Type: application/postscript; name="vacuum.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="vacuum.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.90a Copyright 2002 Radical Eye Software %%Title: C:\LATEX\these\vacuum\vacuum.dvi %%CreationDate: Fri Mar 05 10:34:42 2004 %%Pages: 39 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: CMBX12 CMSY8 CMR10 CMTI10 CMBX10 CMMI10 CMR7 CMR8 %%+ CMSY10 CMEX10 CMMI8 CMMIB10 MSBM10 CMSY6 CMR9 MSBM7 CMR6 EUFM10 %%+ CMMI6 MSAM10 EUFM7 CMMIB7 CMTT10 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips C:\LATEX\these\vacuum\vacuum.dvi %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2004.03.05:1034 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{ rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{ /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{ A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse} ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: texps.pro %! 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMIB7 %!PS-AdobeFont-1.1: CMMIB7 001.100 %%CreationDate: 1996 Jul 27 07:35:50 % Computer Modern fonts were designed by Donald E. Knuth. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (001.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMIB7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMMIB7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put readonly def /FontBBox{0 -250 1294 750}readonly def /UniqueID 5087389 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0525392EECAC163E584A9104D99AD0BC 1B1844A0E222653FA481B8809B26A46F4C483A5D7E95816EA6582584156CFEDE B994ADCFF4645140E3617E4D7E1B0E4541CB9F562E55829B4DD880AABE2229E9 4A9FA259A734D29BBA91BA1E2055CBEA4339BCBFF98D32CEFF11F296225CAABA DCA10577A5D431B714726C1278D8101ABD1BD8D0BD0174FFF9148F8C61C241D9 2AD360A28616CB4A0670BAB68BB2A3981BBAA823C8858EF31989BDBABDF4098A E4EF75BB1764F1578F9CFAAF2948789888274ABDFD1043B1979B55446F38D4A9 BEE0FA78F366D6A169A173AA6011E82B445A8797E37C48107C750383AAB274E4 8EA55C83AFBD4D7CA454D8D0B21B556D7ACB02B73A82444FA1B1D6F5BD26D69D E9E4C809F92B4A969F8953AE78FFDBF365F24DE9C46852EF06999ACF1AF23DCA C20F84FEEB9BFC15D6796CC805729E436B6D4FFAE09F971F0B863021CD0AA3DD 648543DB7B2919D93A47C7BE06FA63199D2697B931F831AB560D301B759E72C7 0B9B20F9955B9D4EB96888A7F16B7B75E10C7F9B415D1443A152450E84669799 8BFC554C45650CDE076205E109A1E3D453664BA189E4E782FC320A7D64C140B5 1A9805779CF1E5E3A2472704B86C7063EA80DEB00782DF225A155AA968A78D8E 7A7D6349517378B46444669ACF48916FB453EA83799897FF177D6479B1C4D74E DDC0E907586009102FDEFD1CFAEE2798FBA979DF5C292454A6B5423F01C6923B 22A74651C32CBA3434D016D9659A5DEE6CB6D7AAEC53858197D177D3E2CE658C 0C09E5DA54E975FEF16EBB05EF82698407D3AE2C29A773FE41B535035FAF1882 964518468C3D0C7FA4618555F52670EF9E09C975A2AAEA4A3FF91290CD705070 6C97C740FD7F1FC881D1190D4346DFBF5591DD5CF6B37DF81109B347FC9751D5 4E02ACE998F1498CC1F441D3667571369CCBBE584F28D5903482AD0A907FE9D3 EBEF19D6284A5D738000A435B451557F3C45C86688ECC78A11486C27E6971F3F 9FE749AB5ADB2F89F84151779EB54380793E5FAC6296D5821F1DFC9EEB29DCD2 B64E03F4CEA84844C4FB7D0DB844ACE08F8DE274DFAABF14A5D3BDE667C4DF9D A704D91A3CC98E1AF521B143393BDCD349EA382A981D2DE070923A7263346182 E121EF2FB250692B3C6E1C8D530702F53D2612AB4B9278E652C2F30D0BBFE676 ACC5E30879F220C96C998F6A08A2F50CC4E1578BA0489A4C71C11EB359CA79B7 6293C3AA8D7B90B4FE343BBDE935FB6A0A4D9B55ABBBC991074B9A3FDA30B5E6 A9BCF8753CECFDC48CF9833B64FE89B005CFAC07A31E625D2FAA9590E7F72D61 7FEA1D676FFF3B708919AB029DCCD0FCBF498818E8F194BDE076541A11C49320 5D660645615099B337CC4ADF3B4498873C364EAE954F0E40ECF6E9874BF7404C F60142DF224E908F40A36481DD2AB098F5CE678A565862A9BDD703D1C8CB45CB A78195EC4472C218FE87B32F2E244D18F22DC77F6CCE465AF5A512579076D6CB B514DC48F0C01BDB14D8A54F582707ECB4CC60952E80F82F19C24A07BDD59F68 5DDAE778F04E43288FA7832A086B57EB47B1E0B9B8D8491FCD19CBECBD787044 3172C8DF6210B36211DC8AAC42D8FDF36FBB0C89253F9E9EE4FCD473A9DC0140 DFA0E0D08DD5B124919A8D76151F19D9CBA8DFFB225521FB0CAC494A07040DED 98A8FCCEF8D48F2D134FDAC448C10478CBA6AD0424D929D647973C80C7D0A033 D006270F23C191DD0DC06A77C9D7FF74F3C3B7D2091D3A8388605307410D737B 2C8C90B038 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: EUFM7 %!PS-AdobeFont-1.1: EUFM7 2.1 %%CreationDate: 1992 Nov 20 17:36:25 % Euler fonts were designed by Hermann Zapf. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (EUFM7) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /EUFM7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 83 /S put readonly def /FontBBox{0 -250 1193 750}readonly def /UniqueID 5031992 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMBX10 %!PS-AdobeFont-1.1: CMBX10 1.00B %%CreationDate: 1992 Feb 19 19:54:06 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 12 /fi put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 76 /L put dup 78 /N put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 87 /W put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put readonly def /FontBBox{-301 -250 1164 946}readonly def /UniqueID 5000768 def currentdict end currentfile eexec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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSAM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSAM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 38 /greaterorsimilar put readonly def /FontBBox{8 -463 1331 1003}readonly def /UniqueID 5031981 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI6 %!PS-AdobeFont-1.1: CMMI6 1.100 %%CreationDate: 1996 Jul 23 07:53:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 18 /theta put dup 39 /phi1 put dup 59 /comma put dup 61 /slash put dup 69 /E put dup 81 /Q put dup 82 /R put dup 106 /j put dup 107 /k put dup 108 /l put dup 110 /n put dup 112 /p put readonly def /FontBBox{11 -250 1241 750}readonly def /UniqueID 5087381 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 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cleartomark %%EndFont %%BeginFont: EUFM10 %!PS-AdobeFont-1.1: EUFM10 2.1 %%CreationDate: 1992 Nov 20 17:36:20 % Euler fonts were designed by Hermann Zapf. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (EUFM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /EUFM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 83 /S put readonly def /FontBBox{-26 -224 1055 741}readonly def /UniqueID 5031986 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR6 %!PS-AdobeFont-1.1: CMR6 1.0 %%CreationDate: 1991 Aug 20 16:39:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 3 /Lambda put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 54 /six put readonly def /FontBBox{-20 -250 1193 750}readonly def /UniqueID 5000789 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: MSBM7 %!PS-AdobeFont-1.1: MSBM7 2.1 %%CreationDate: 1992 Oct 17 08:30:50 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM7) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 67 /C put dup 82 /R put readonly def /FontBBox{0 -504 2615 1004}readonly def /UniqueID 5032014 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR9 %!PS-AdobeFont-1.1: CMR9 1.0 %%CreationDate: 1991 Aug 20 16:39:59 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 19 /acute put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 52 /four put dup 53 /five put dup 57 /nine put dup 58 /colon put dup 66 /B put dup 67 /C put dup 70 /F put dup 76 /L put dup 77 /M put dup 79 /O put dup 80 /P put dup 83 /S put dup 94 /circumflex put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 104 /h put dup 105 /i put dup 109 /m put dup 110 /n put dup 111 /o put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 120 /x put dup 121 /y put readonly def /FontBBox{-39 -250 1036 750}readonly def /UniqueID 5000792 def currentdict end currentfile eexec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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 67 /C put dup 72 /H put dup 82 /R put dup 92 /hatwider put dup 126 /planckover2pi1 put readonly def /FontBBox{-55 -420 2343 920}readonly def /UniqueID 5031982 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF5B8CABB9FFC6A66A4000A13D5F68BFF326D 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cleartomark %%EndFont %%BeginFont: CMMIB10 %!PS-AdobeFont-1.1: CMMIB10 1.100 %%CreationDate: 1996 Jul 23 07:54:00 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMIB10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMIB10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put readonly def /FontBBox{-15 -250 1216 750}readonly def /UniqueID 5087392 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI8 %!PS-AdobeFont-1.1: CMMI8 1.100 %%CreationDate: 1996 Jul 23 07:53:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 12 /beta put dup 13 /gamma put dup 14 /delta put dup 15 /epsilon1 put dup 16 /zeta put dup 18 /theta put dup 20 /kappa put dup 25 /pi put dup 26 /rho put dup 32 /psi put dup 39 /phi1 put dup 58 /period put dup 59 /comma put dup 61 /slash put dup 66 /B put dup 67 /C put dup 69 /E put dup 72 /H put dup 73 /I put dup 74 /J put dup 76 /L put dup 77 /M put dup 80 /P put dup 81 /Q put dup 82 /R put dup 84 /T put dup 90 /Z put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 112 /p put dup 113 /q put dup 115 /s put dup 116 /t put dup 117 /u put dup 120 /x put dup 121 /y put readonly def /FontBBox{-24 -250 1110 750}readonly def /UniqueID 5087383 def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 1 /periodcentered put dup 2 /multiply put dup 3 /asteriskmath put dup 8 /circleplus put dup 10 /circlemultiply put dup 15 /bullet put dup 20 /lessequal put dup 21 /greaterequal put dup 24 /similar put dup 26 /propersubset put dup 27 /propersuperset put dup 33 /arrowright put dup 39 /similarequal put dup 41 /arrowdblright put dup 49 /infinity put dup 50 /element put dup 54 /negationslash put dup 55 /mapsto put dup 56 /universal put dup 59 /emptyset put dup 60 /Rfractur put dup 65 /A put dup 66 /B put dup 67 /C put dup 69 /E put dup 70 /F put dup 72 /H put dup 80 /P put dup 81 /Q put dup 82 /R put dup 88 /X put dup 89 /Y put dup 91 /union put dup 92 /intersection put dup 94 /logicaland put dup 102 /braceleft put dup 103 /braceright put dup 104 /angbracketleft put dup 105 /angbracketright put dup 106 /bar put dup 112 /radical put dup 114 /nabla put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueID 5000820 def currentdict end currentfile eexec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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 12 /beta put dup 13 /gamma put dup 14 /delta put dup 15 /epsilon1 put dup 16 /zeta put dup 17 /eta put dup 18 /theta put dup 20 /kappa put dup 22 /mu put dup 24 /xi put dup 25 /pi put dup 26 /rho put dup 27 /sigma put dup 31 /chi put dup 32 /psi put dup 39 /phi1 put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 64 /partialdiff put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 90 /Z put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-32 -250 1048 750}readonly def /UniqueID 5087385 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958 9E394A533A081C36D456A09920001A3D2199583EB9B84B4DEE08E3D12939E321 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cleartomark %%EndFont %%BeginFont: CMBX12 %!PS-AdobeFont-1.1: CMBX12 1.0 %%CreationDate: 1991 Aug 20 16:34:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 19 /acute put dup 38 /ampersand put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 56 /eight put dup 58 /colon put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 72 /H put dup 73 /I put dup 76 /L put dup 77 /M put dup 78 /N put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 87 /W put dup 90 /Z put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-53 -251 1139 750}readonly def /UniqueID 5000769 def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR7 %!PS-AdobeFont-1.1: CMR7 1.0 %%CreationDate: 1991 Aug 20 16:39:21 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 48 /zero put readonly def /FontBBox{-27 -250 1122 750}readonly def /UniqueID 5000790 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR10 %!PS-AdobeFont-1.1: CMR10 1.00B %%CreationDate: 1992 Feb 19 19:54:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /Gamma put dup 1 /Delta put dup 3 /Lambda put dup 9 /Psi put dup 10 /Omega put dup 11 /ff put dup 12 /fi put dup 14 /ffi put dup 19 /acute put dup 34 /quotedblright put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 61 /equal put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 94 /circumflex put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /endash put dup 127 /dieresis put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueID 5000793 def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMTI10 %!PS-AdobeFont-1.1: CMTI10 1.00B %%CreationDate: 1992 Feb 19 19:56:16 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 12 /fi put dup 18 /grave put dup 19 /acute put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 54 /six put dup 55 /seven put dup 58 /colon put dup 64 /at put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 72 /H put dup 73 /I put dup 74 /J put dup 76 /L put dup 77 /M put dup 78 /N put dup 80 /P put dup 81 /Q put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 90 /Z put dup 91 /bracketleft put dup 93 /bracketright put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /endash put readonly def /FontBBox{-163 -250 1146 969}readonly def /UniqueID 5000828 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958 9E3948FFB0B4E70F212EC976D65099D84E0D37A7A771C3101D6AD26A0513378F 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3420 211 4 v 1550 3504 a(\(2)p Fs(\031)s Fz(\))1720 3477 y Fr(3)1786 3317 y Fp(Z)9 b(Z)1897 3524 y FA(j)p Fo(p)p FA(j)p Fo(;)p FA(j)p Fo(q)r FA(j\024)p Fr(\003)2187 3441 y Fz(T)-8 b(r)2281 3461 y Fj(C)2329 3442 y Fi(4)2383 3340 y Fp(\020)2440 3418 y(b)2437 3441 y Fz(\000\()p Fs(p;)15 b(q)s Fz(\))2694 3340 y Fp(\021)2749 3441 y Fs(e)2791 3404 y Fo(ix)p Fr(\()p Fo(p)p FA(\000)p Fo(q)r Fr(\))3039 3441 y Fs(dp)g(dq)428 b Fz(\(6\))0 3700 y(so)31 b(that)864 3832 y Fp(b)-57 b Fs(\032)905 3846 y Fr(\000)953 3832 y Fz(\()p Fs(k)s Fz(\))27 b(=)1323 3770 y(1)p 1206 3811 282 4 v 1206 3898 a(\(2)p Fs(\031)s Fz(\))1376 3872 y Fr(3)p Fo(=)p Fr(2)1512 3708 y Fp(Z)1562 3914 y FA(j)p Fo(p)p FA(j\024)p Fr(\003)1760 3832 y Fz(T)-8 b(r)1854 3852 y Fj(C)1902 3833 y Fi(4)1956 3731 y Fp(\020)2013 3809 y(b)2010 3832 y Fz(\000\()p Fs(p)20 b Fz(+)g Fs(k)s(=)p Fz(2)p Fs(;)15 b(p)22 b Fq(\000)d Fs(k)s(=)p Fz(2\))2772 3731 y Fp(\021)2828 3832 y Fs(dp)0 4067 y Fz(sho)m(wing)31 b(that)38 b Fp(b)-57 b Fs(\032)592 4081 y Fr(\000)667 4067 y Fq(2)26 b Fs(L)816 4034 y Fr(1)855 4067 y Fz(,)32 b(and)e(so)i Fs(\032)1249 4081 y Fr(\000)1323 4067 y Fq(2)27 b(C)1464 4034 y Fr(0)1459 4092 y(0)1503 4067 y Fz(.)43 b(Notice)33 b(that)f(\(6\))g(sho)m(ws)f(that)h(the)f (function)g(\000)c Fq(2)f Fh(S)3422 4081 y Fr(2)3461 4067 y Fz(\()p Fq(H)3573 4081 y Fr(\003)3627 4067 y Fz(\))h Fq(7!)0 4180 y Fs(\032)47 4194 y Fr(\000)120 4180 y Fq(2)e(C)259 4147 y Fr(0)254 4205 y(0)319 4180 y Fq(\\)20 b Fs(L)462 4147 y Fr(2)501 4180 y Fz(\()p Fm(R)602 4147 y Fr(3)642 4180 y Fz(\))30 b(is)h(con)m(tin)m(uous.)141 4293 y(In)e(the)i(next)f (subsection,)g(w)m(e)h(pro)m(v)m(e)g(that)f Fq(E)39 b Fz(is)30 b(w)m(ell-de\014ned)g(and)f(b)s(ounded)f(from)i(b)s(elo)m(w)g (on)g Fq(B)3535 4307 y Fr(\003)3588 4293 y Fz(.)40 b(W)-8 b(e)0 4406 y(then)31 b(sho)m(w)f(the)i(existence)g(of)f(a)h(minimizer,) f(whic)m(h)g(can)g(b)s(e)f(in)m(terpreted)h(as)h(a)f(stable)h(p)s (olarized)f(v)-5 b(acuum)0 4519 y(in)30 b(the)h(BDF)g(appro)m (ximation.)141 4681 y(T)-8 b(o)29 b(this)g(end,)f(let)i(us)e(\014rst)f (explain)i(ho)m(w)g(this)f(energy)h(is)g(used)f(in)g([5)q(].)40 b(In)28 b(the)g(BDF)i(setting,)g(a)f(state)h(of)0 4794 y(the)h(system)f(is)g(a)h(pair)f(\()p Fs(P)s(;)15 b(\015)5 b Fz(\))32 b(where)136 4979 y Fq(\017)46 b Fs(P)e Fz(is)30 b(a)h(pro)5 b(jector)31 b(suc)m(h)f(that)h Fs(Q)25 b Fz(=)g Fs(P)33 b Fq(\000)20 b Fs(P)1736 4946 y Fr(0)1801 4979 y Fq(2)k Fh(S)1961 4993 y Fr(2)2001 4979 y Fz(\()p Fq(H)2113 4993 y Fr(\003)2166 4979 y Fz(\),)31 b(represen)m(ting)g(the) f(dressed)g(v)-5 b(acuum,)136 5165 y Fq(\017)46 b Fs(\015)51 b Fq(2)45 b Fh(S)506 5179 y Fr(1)546 5165 y Fz(\()p Fq(H)658 5179 y Fr(\003)711 5165 y Fz(\))e(is)g(the)g(densit)m(y)g(matrix)g(of)g (a)g Fs(B)5 b(D)s(F)13 b Fz(-state)43 b(built)g(with)f(electrons)i(and) e(p)s(ositrons)227 5278 y(de\014ned)29 b(b)m(y)i Fs(P)13 b Fz(.)40 b(This)30 b(means)g(that)1755 5391 y Fs(\015)g Fz(=)25 b Fs(\015)1975 5405 y Fr(+)2055 5391 y Fq(\000)20 b Fs(\015)2193 5405 y FA(\000)227 5556 y Fz(where)29 b Fs(\015)536 5570 y Fr(+)624 5556 y Fz(and)f Fs(\015)846 5570 y FA(\000)934 5556 y Fz(are)h(pro)5 b(jectors)29 b(of)g(\014nite)g(rank)f(with)h(Ran\()p Fs(\015)2502 5570 y Fr(+)2561 5556 y Fz(\))d Fq(\032)f Fz(\(1)18 b Fq(\000)f Fs(P)c Fz(\))p Fq(H)3087 5570 y Fr(\003)3169 5556 y Fz(and)28 b(Ran\()p Fs(\015)3589 5570 y FA(\000)3648 5556 y Fz(\))e Fq(\032)227 5669 y Fs(P)13 b Fq(H)375 5683 y Fr(\003)428 5669 y Fz(.)41 b(It)30 b(therefore)h(satis\014es)g Fq(\000)p Fs(P)38 b Fq(\024)25 b Fs(\015)30 b Fq(\024)25 b Fz(1)c Fq(\000)f Fs(P)13 b Fz(.)1867 5906 y(5)p eop end %%Page: 6 6 TeXDict begin 6 5 bop 0 63 a Fz(Details)37 b(are)e(giv)m(en)i(in)d(App) s(endix)g(for)h(the)g(in)m(terested)h(reader.)55 b(The)34 b(densit)m(y)i(matrix)f Fs(\015)40 b Fz(corresp)s(onds)34 b(to)0 176 y(Slater)e(determinan)m(ts)h(in)m(v)m(olving)g(electrons)g (and)f(p)s(ositrons)f(de\014ned)f(b)m(y)i(means)g(of)g(the)g(v)-5 b(acuum)32 b Fs(P)13 b Fz(.)45 b(The)0 289 y(energy)31 b(of)f(suc)m(h)g(a)h(state)h(\()p Fs(P)s(;)15 b(\015)5 b Fz(\))31 b(is)g(then)f(giv)m(en)h(b)m(y)1431 446 y Fq(E)1487 409 y Fr(BDF)1641 446 y Fz(\()p Fs(P)s(;)15 b(\015)5 b Fz(\))27 b(=)e Fq(E)8 b Fz(\()p Fs(Q)20 b Fz(+)g Fs(\015)5 b Fz(\))1315 b(\(7\))0 603 y(where)33 b(w)m(e)i(recall)g(that)g Fs(Q)c Fz(=)g Fs(P)k Fq(\000)23 b Fs(P)1314 570 y Fr(0)1353 603 y Fz(.)52 b(Remark)34 b(that)g(the)g(real)h(ph)m(ysical)g(ob)5 b(ject)34 b(is)g(not)h(really) g(the)f(pair)0 716 y(\()p Fs(P)s(;)15 b(\015)5 b Fz(\),)28 b(but)e(the)h(sum)e(\000)g(=)g Fs(Q)12 b Fz(+)g Fs(\015)30 b Fz(=)25 b Fs(P)g Fq(\000)12 b Fs(P)1535 683 y Fr(0)1587 716 y Fz(+)g Fs(\015)5 b Fz(.)39 b(It)27 b(ful\014lls)e Fq(\000)p Fs(P)2289 683 y Fr(0)2354 716 y Fq(\024)g Fz(\000)g Fq(\024)g Fz(1)12 b Fq(\000)g Fs(P)2839 683 y Fr(0)2879 716 y Fz(.)39 b(Therefore)26 b(the)h(set)f Fq(B)3701 730 y Fr(\003)3754 716 y Fz(,)0 829 y(on)33 b(whic)m(h)h Fq(E)41 b Fz(is)34 b(de\014ned,)f(is)g(seen)h(to)g(b)s(e)f(the)h(con)m 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b(a)g(Hilb)-5 b(ert-Schmidt)35 b(op)-5 b(er)g(ator.)0 1429 y(Then)33 b Fs(Q)f Fy(is)h(sup)-5 b(ertr)g(ac)g(e-class)35 b(with)f(r)-5 b(esp)g(e)g(ct)34 b(to)f Fs(P)1761 1396 y Fr(0)1800 1429 y Fy(.)42 b(Mor)-5 b(e)g(over,)34 b Fz(str)2405 1449 y Fo(P)2460 1430 y Fi(0)2498 1429 y Fz(\()p Fs(Q)p Fz(\))f Fy(is)g(an)g(inte)-5 b(ger)33 b(which)g(satis\014es)1280 1586 y Fq(8)p Fs(n)24 b Fq(\025)h Fz(1)p Fs(;)49 b Fz(str)1731 1606 y Fo(P)1786 1587 y Fi(0)1825 1586 y Fz(\()p Fs(Q)p Fz(\))25 b(=)g(tr\()p Fs(Q)2266 1549 y Fr(2)p Fo(n)p Fr(+1)2439 1586 y Fz(\))p Fs(:)141 1743 y Fy(Pr)-5 b(o)g(of)34 b({)62 b Fz(W)-8 b(e)31 b(ha)m(v)m(e)g Fs(Q)930 1710 y Fr(2)995 1743 y Fz(=)25 b Fs(P)32 b Fq(\000)19 b Fs(P)13 b(P)1413 1710 y Fr(0)1471 1743 y Fq(\000)19 b Fs(P)1632 1710 y Fr(0)1672 1743 y Fs(P)32 b Fz(+)19 b Fs(P)1923 1710 y Fr(0)1988 1743 y Fz(=)25 b(\(1)20 b Fq(\000)e Fs(P)2344 1710 y Fr(0)2384 1743 y Fz(\))p Fs(Q)p Fz(\(1)i Fq(\000)f Fs(P)2752 1710 y Fr(0)2791 1743 y Fz(\))h Fq(\000)f Fs(P)3007 1710 y Fr(0)3046 1743 y Fs(QP)3189 1710 y Fr(0)3229 1743 y Fz(.)40 b(This)29 b(implies)0 1856 y(that)i(\(1)21 b Fq(\000)f Fs(P)460 1823 y Fr(0)499 1856 y Fz(\))p Fs(Q)p Fz(\(1)i Fq(\000)d Fs(P)869 1823 y Fr(0)909 1856 y Fz(\))31 b(and)e Fq(\000)p Fs(P)1293 1823 y Fr(0)1332 1856 y Fs(QP)1475 1823 y Fr(0)1545 1856 y Fz(are)i(non-negativ)m(e)h(trace-class)h(op)s (erators.)141 1969 y(W)-8 b(e)47 b(no)m(w)e(use)g(the)g(pro)s(of)g(of)g ([1)q(,)k(Theorem)c(4.1].)87 b(Since)45 b Fs(Q)50 b Fq(2)g Fh(S)2587 1983 y Fr(2)2627 1969 y Fz(,)f(w)m(e)d(infer)e Fs(Q)3146 1936 y Fr(3)3236 1969 y Fq(2)50 b Fh(S)3422 1983 y Fr(1)3507 1969 y Fz(and)44 b(so)0 2082 y(\()p Fs(P)s(;)15 b(P)207 2049 y Fr(0)247 2082 y Fz(\))34 b(is)f(a)h(F)-8 b(redholm)33 b(pair,)h(in)f(the)h(language)h(of)e([1)q(].)50 b(Therefore,)34 b(tr\()p Fs(Q)2660 2049 y Fr(3)2699 2082 y Fz(\))g(is)f(an)h(in)m(teger)g(and)f(satis\014es)0 2195 y(tr\()p Fs(Q)178 2162 y Fr(3)218 2195 y Fz(\))25 b(=)g(tr\()p Fs(Q)552 2162 y Fr(2)p Fo(n)p 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y FA(0)548 2872 y Fr(+)607 2850 y Fs(AP)746 2812 y FA(0)733 2872 y Fr(+)793 2850 y Fz(])25 b(=)g(tr[)p Fs(A)p Fz(\()p Fs(P)1209 2812 y FA(0)1196 2872 y Fr(+)1277 2850 y Fq(\000)20 b Fs(P)1426 2864 y Fr(+)1485 2850 y Fz(\)])h(+)f(tr[)p Fs(P)1811 2864 y Fr(+)1870 2850 y Fs(AP)1996 2864 y Fr(+)2056 2850 y Fz(])25 b(=)g Fq(\000)15 b Fz(tr[)p Fs(A)p Fz(\()p Fs(P)2558 2812 y FA(0)2603 2850 y Fq(\000)k Fs(P)13 b Fz(\)])21 b(+)f(tr[)p Fs(P)3090 2864 y Fr(+)3150 2850 y Fs(AP)3276 2864 y Fr(+)3335 2850 y Fz(])p Fs(;)0 3034 y Fz(where)32 b(w)m(e)g(ha)m(v)m(e)i(used)d(the)i(notation)g Fs(P)1403 3048 y Fr(+)1491 3034 y Fz(=)28 b(1)22 b Fq(\000)f Fs(P)45 b Fz(and)32 b Fs(P)2102 3001 y FA(0)2089 3056 y Fr(+)2177 3034 y Fz(=)c(1)22 b Fq(\000)f Fs(P)2506 3001 y FA(0)2529 3034 y Fz(.)47 b(Summing)31 b(this)h(t)m(w)m(o)h (results,)g(w)m(e)0 3147 y(obtain)e(the)f(form)m(ula)h(str)880 3161 y Fo(P)938 3147 y Fz([)p Fs(A)p Fz(])26 b(=)f(str)1285 3162 y Fo(P)1340 3143 y Fl(0)1366 3147 y Fz([)p Fs(A)p Fz(].)p 3714 3147 4 62 v 3718 3088 55 4 v 3718 3147 V 3771 3147 4 62 v 0 3417 a FB(3.2)112 b(Preliminaries)0 3598 y Fz(T)-8 b(o)31 b(pro)m(v)m(e)g(Theorem)f(3,)h(w)m(e)g(need)f (the)h(follo)m(wing)0 3805 y Fe(Lemma)k(2.)42 b Fy(Assume)32 b(that)i Fs(')25 b Fz(=)g Fs(\032)c Fq(\003)1354 3770 y Fr(1)p 1342 3785 59 4 v 1342 3838 a FA(j\001j)1444 3805 y Fy(for)33 b(some)g Fs(\032)25 b Fq(2)g(C)5 b Fy(.Then)579 4037 y Fq(j)-15 b(jr)p Fs(')p Fq(j)g(j)785 4064 y Fo(H)848 4045 y Fi(1)912 4037 y Fz(=)25 b(4)p Fs(\031)s Fq(j)-15 b(j)p Fs(\032)p Fq(j)g(j)1225 4051 y FA(C)1271 4037 y Fs(;)201 b Fq(j)-15 b(j)q Fs(')p Fq(j)g(j)1627 4064 y Fo(L)1675 4045 y Fl(1)1770 4037 y Fq(\024)25 b Fs(C)1931 4051 y FA(1)2005 4037 y Fz(4)p Fs(\031)s Fq(j)-15 b(j)p Fs(\032)p Fq(j)g(j)2222 4051 y FA(C)2269 4037 y Fs(;)201 b Fq(j)-15 b(j)p Fs(')p Fq(j)h(j)2625 4064 y Fo(L)2673 4045 y Fi(6)2737 4037 y Fq(\024)25 b Fs(C)2898 4051 y Fr(6)2938 4037 y Fz(4)p Fs(\031)s Fq(j)-15 b(j)p Fs(\032)p Fq(j)g(j)3155 4051 y FA(C)0 4255 y 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5103 y Fp(\023)2759 5126 y Fr(1)p Fo(=)p Fr(2)2885 5231 y Fz(4)p Fs(\031)s Fq(j)-15 b(j)p Fs(\032)p Fq(j)g(j)3102 5245 y FA(C)3148 5231 y Fs(:)0 5462 y Fz(The)30 b(rest)g(is)h(easily)g (obtained)g(b)m(y)f(the)h(Sob)s(olev)f(inequalities.)p 3714 5462 4 62 v 3718 5404 55 4 v 3718 5462 V 3771 5462 4 62 v 0 5669 a Fe(Lemma)35 b(3.)42 b Fy(L)-5 b(et)32 b Fs(P)46 b Fy(b)-5 b(e)32 b(a)h(pr)-5 b(oje)g(ctor)35 b(such)e(that)h Fs(P)f Fq(\000)20 b Fs(P)1971 5636 y Fr(0)2036 5669 y Fq(2)25 b(A)2195 5683 y Fr(\003)2247 5669 y Fy(.)42 b(Then)33 b Fs(D)2629 5683 y Fo(Q)2722 5669 y Fy(is)f(b)-5 b(ounde)g(d.)1867 5906 y Fz(9)p eop end %%Page: 10 10 TeXDict begin 10 9 bop 141 76 a Fy(Pr)-5 b(o)g(of)37 b({)70 b Fz(Due)34 b(to)g(the)g(cut-o\013)g(in)g(F)-8 b(ourier)34 b(space,)h Fs(D)2038 43 y Fr(0)2111 76 y Fz(is)e(b)s(ounded)f(on)h Fq(H)2786 90 y Fr(\003)2839 76 y Fz(.)51 b(On)32 b(the)i(other)g(hand,)f(if)0 189 y Fs(')f Fz(=)f Fs(\032)23 b Fq(\003)353 153 y Fr(1)p 341 168 59 4 v 341 221 a FA(j\001j)444 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b(will)i(end)e(the)h(pro)s(of)f (since)h(the)g(other)g(term)g(is)0 3687 y(trace-class.)75 b(The)40 b(general)i(idea)g(of)f(the)g(pro)s(of)f(is)h(to)h(appro)m (ximate)g(\000)f(b)m(y)g(a)g(trace-class)i(op)s(erator)f(for)0 3800 y(whic)m(h)33 b(this)g(equalit)m(y)h(is)f(true,)h(and)e(to)i(pass) f(to)g(the)h(limit.)49 b(Ho)m(w)m(ev)m(er,)36 b(the)d(b)s(eha)m(viour)g (of)g(the)g(asso)s(ciated)0 3913 y(densit)m(y)e(in)g(the)h(space)f Fq(C)37 b Fz(is)31 b(not)g(ob)m(vious)h(and)e(to)i(o)m(v)m(ercome)i (this)d(di\016cult)m(y)-8 b(,)32 b(w)m(e)g(shall)f(also)h(appro)m (ximate)0 4026 y(the)f(densit)m(y)g Fs(\032)518 3993 y FA(0)518 4053 y Fo(Q)608 4026 y Fz(to)g(obtain)g(a)g(p)s(oten)m(tial) h(in)e Fs(L)1630 3993 y Fr(2)1670 4026 y Fz(\()p Fm(R)1771 3993 y Fr(3)1810 4026 y Fz(\).)42 b(W)-8 b(e)32 b(th)m(us)e(start)h(b)m (y)f(c)m(ho)s(osing)i(a)f(sequence)g Fs(\032)3483 4040 y Fo(j)3550 4026 y Fz(whic)m(h)0 4152 y(con)m(v)m(erges)d(as)e Fs(j)31 b Fq(!)25 b Fz(+)p Fq(1)g Fz(to)i Fs(\032)1035 4119 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1528 y Fo(j)1503 1502 y Fq(\000)20 b Fs(P)1665 1469 y Fr(0)1729 1502 y Fq(2)25 b Fh(S)1890 1516 y Fr(2)1960 1502 y Fz(b)m(y)31 b([21)q(].)41 b(No)m(w,)31 b(using)g(\(12\))r(,)f(it)h(is)g(easily)g(seen)g(that)0 1615 y Fs(P)71 1582 y FA(0)58 1641 y Fo(j)95 1615 y Fz(\000)152 1582 y Fo(n)199 1615 y Fs(P)270 1582 y FA(0)257 1641 y Fo(j)319 1615 y Fq(!)25 b Fs(P)506 1582 y FA(0)493 1641 y Fo(j)530 1615 y Fz(\000)p Fs(P)658 1582 y FA(0)645 1641 y Fo(j)710 1615 y Fz(and)i(\(1)16 b Fq(\000)f Fs(P)1137 1582 y FA(0)1124 1641 y Fo(j)1161 1615 y Fz(\)\000)1253 1582 y Fo(n)1300 1615 y Fz(\(1)i Fq(\000)e Fs(P)1554 1582 y FA(0)1541 1641 y Fo(j)1578 1615 y Fz(\))26 b Fq(!)f Fz(\(1)16 b Fq(\000)f Fs(P)2008 1582 y FA(0)1995 1641 y Fo(j)2032 1615 y Fz(\)\000\(1)i Fq(\000)e Fs(P)2378 1582 y FA(0)2365 1641 y Fo(j)2402 1615 y Fz(\))28 b(in)g Fh(S)2644 1629 y Fr(1)2711 1615 y Fz(as)h Fs(n)24 b Fq(!)i(1)p Fz(,)i(since)h(this)f(terms)0 1728 y(can)g(b)s(e)g(expanded)f(as)h(a)g (sum)f(of)i(trace-class)h(op)s(erators)e(and)f(pro)s(ducts)g(of)h(at)h (least)g(t)m(w)m(o)g(Hilb)s(ert-Sc)m(hmidt)0 1841 y(op)s(erators)i(con) m(v)m(erging)i(strongly)e(in)f Fh(S)1389 1855 y Fr(2)1429 1841 y Fz(.)42 b(Since)31 b Fs(D)1809 1855 y Fo(j)1877 1841 y Fz(is)g(b)s(ounded)d(b)m(y)j(the)g(pro)s(of)f(of)h(Lemma)g(3,)h (w)m(e)f(obtain)0 1954 y(that)g(str)304 1973 y Fo(P)359 1950 y Fl(0)349 1995 y Fg(j)385 1954 y Fz(\()p Fs(D)495 1968 y Fo(j)532 1954 y Fz(\000)589 1921 y Fo(n)636 1954 y Fz(\))26 b Fq(!)788 1968 y Fo(n)p FA(!1)1001 1954 y Fz(str)1108 1973 y Fo(P)1163 1950 y Fl(0)1153 1995 y Fg(j)1189 1954 y Fz(\()p Fs(D)1299 1968 y Fo(j)1336 1954 y Fz(\000\))g(=)f(str)1657 1974 y Fo(P)1712 1955 y Fi(0)1750 1954 y Fz(\()p Fs(D)1860 1968 y Fo(j)1897 1954 y Fz(\000\))30 b(b)m(y)h(Theorem)f(1.)141 2081 y(As)h(a)f(conclusion,)i(w)m(e)f(ha)m (v)m(e)g(pro)m(v)m(ed)g(\(15\))h(for)e(all)i(\000)25 b Fq(2)g(A)2155 2095 y Fr(\003)2208 2081 y Fz(.)41 b(T)-8 b(o)31 b(\014nish)e(the)h(pro)s(of,)g(it)h(remains)g(to)g(pass)0 2194 y(to)g(the)g(limit)g(as)f Fs(j)h Fq(!)26 b Fz(+)p Fq(1)p Fz(.)40 b(Since)1474 2220 y Fp(Z)1524 2426 y Fj(R)1572 2408 y Fi(3)1626 2344 y Fs(\032)1673 2358 y Fr(\000)1721 2344 y Fs(')1780 2358 y Fo(j)1842 2344 y Fz(=)25 b Fs(D)s Fz(\()p Fs(\032)2098 2358 y Fr(\000)2147 2344 y Fs(;)15 b(\032)2234 2358 y Fo(j)2271 2344 y Fz(\))0 2556 y(and)30 b Fs(\032)224 2570 y Fr(\000)299 2556 y Fq(2)c(C)36 b Fz(\(recall)c(that)g(\000)26 b Fq(2)g(A)1189 2570 y Fr(\003)1242 2556 y Fz(\),)31 b Fs(\032)1380 2570 y Fo(j)1443 2556 y Fq(!)26 b Fs(\032)1607 2523 y FA(0)1607 2583 y Fo(Q)1698 2556 y Fz(strongly)31 b(in)g Fq(C)36 b Fz(as)31 b Fs(j)h Fq(!)26 b(1)p Fz(,)31 b(w)m(e)h(ma)m(y)g(pass)e(to)i(the)f(limit)h(in)0 2669 y(the)c(left)g(hand)f(side)h(of)35 b(\(15\))q(.)40 b(T)-8 b(o)28 b(pass)f(to)i(the)f(limit)g(in)g(the)g(righ)m(t)g(hand)f (side,)h(w)m(e)g(use)g(again)g(the)g(fact)h(that)540 2868 y(str)646 2887 y Fo(P)701 2868 y Fi(0)9 b Fz(\()p 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b Fq(\000)22 b Fs(P)660 1915 y Fr(0)732 1948 y Fz(is)34 b(a)g(minimizer)f(of)g Fq(E)42 b Fz(in)33 b Fq(B)1698 1962 y Fr(\003)1751 1948 y Fz(.)49 b(W)-8 b(e)35 b(therefore)e(ha)m(v)m(e)i(for)e(all)h Fs(\015)h Fq(2)30 b Fh(S)3101 1962 y Fr(1)3163 1948 y Fq(\\)22 b(A)3319 1962 y Fr(\003)3405 1948 y Fz(suc)m(h)33 b(that)0 2061 y Fq(\000)p Fs(P)38 b Fq(\024)25 b Fs(\015)30 b Fq(\024)25 b Fz(1)c Fq(\000)f Fs(P)1549 2174 y Fq(E)8 b Fz(\()p Fs(Q)20 b Fz(+)g Fs(\015)5 b Fz(\))26 b Fq(\025)f(E)8 b Fz(\()p Fs(Q)p Fz(\))0 2339 y(or)30 b(equiv)-5 b(alen)m(tly)458 2590 y Fq(E)514 2552 y FA(0)538 2590 y Fz(\()p Fs(\015)5 b Fz(\))26 b(:=)f(tr)15 b(\()p Fs(D)1003 2604 y Fo(Q)1063 2590 y Fs(\015)5 b Fz(\))21 b(+)1272 2528 y Fs(\013)p 1272 2569 59 4 v 1279 2652 a Fz(2)1355 2466 y Fp(Z)10 b(Z)1532 2528 y Fs(\032)1579 2542 y Fo(\015)1623 2528 y Fz(\()p Fs(x)p Fz(\))p Fs(\032)1792 2542 y Fo(\015)1838 2528 y Fz(\()p Fs(y)s Fz(\))p 1532 2569 425 4 v 1613 2652 a Fq(j)p Fs(x)21 b Fq(\000)f Fs(y)s Fq(j)1966 2590 y Fs(dx)15 b(dy)24 b Fq(\000)2297 2528 y Fs(\013)p 2297 2569 59 4 v 2304 2652 a Fz(2)2380 2466 y Fp(Z)10 b(Z)2557 2528 y Fq(j)p Fs(\015)5 b Fz(\()p Fs(x;)15 b(y)s Fz(\))p Fq(j)2869 2495 y Fr(2)p 2557 2569 353 4 v 2603 2652 a Fq(j)p Fs(x)20 b Fq(\000)g Fs(y)s Fq(j)2920 2590 y Fs(dx)15 b(dy)29 b Fq(\025)c Fz(0)p Fs(:)297 b Fz(\(17\))0 2839 y(W)-8 b(e)23 b(no)m(w)e(follo)m(w)i(the)e(pro)s(of)g(of)h(Theorem)f(4) g(b)m(y)h(Bac)m(h)g Fy(et)j(al.)38 b Fz([2].)g(Their)21 b(pro)s(of)g(is)g(done)g(with)g Fs(D)3252 2853 y Fo(Q)3334 2839 y Fz(replaced)h(b)m(y)0 2952 y Fs(D)78 2919 y Fo(\013')202 2952 y Fz(but)27 b(they)i(also)g(men)m(tion)h(that)f(it)g(can)f(b)s(e)g (extended)h(to)g(a)g(more)f(general)i(case,)g(pro)m(vided)e(0)36 b Fs(=)-55 b Fq(2)25 b Fs(\033)s Fz(\()p Fs(D)3684 2966 y Fo(Q)3744 2952 y Fz(\))0 3065 y(and)k Fs(P)13 b Fz(,)31 b(1)19 b Fq(\000)g Fs(P)43 b Fz(lea)m(v)m(e)33 b(the)d(domain)g(of)g Fs(D)1440 3079 y Fo(Q)1529 3065 y Fz(in)m(v)-5 b(arian)m(t,)32 b(whic)m(h)e(is)g(the)g(case)h(here.)40 b(Let)31 b(us)e(ho)m(w)m(ev)m (er)i(explain)0 3178 y(the)g(general)g(ideas)g(of)f(this)h(pro)s(of)e (for)h(the)h(reader's)f(con)m(v)m(enience.)141 3291 y(If)42 b Fs(P)56 b Fz(do)s(es)42 b(not)h(comm)m(ute)h(with)e Fs(\037)1429 3309 y Fr(\()p FA(\0001)p Fr(;0\))1668 3291 y Fz(\()p Fs(D)1778 3305 y Fo(Q)1839 3291 y Fz(\),)k(then)c(there)h (exist)h(t)m(w)m(o)g(normalized)f(v)m(ectors)h Fs(f)55 b Fq(2)0 3404 y Fz(\(1)21 b Fq(\000)f Fs(P)13 b Fz(\))p Fq(H)375 3418 y Fr(\003)458 3404 y Fz(and)30 b Fs(g)f Fq(2)c Fs(P)13 b Fq(H)941 3418 y Fr(\003)1024 3404 y Fz(suc)m(h)30 b(that)h(the)g(real)g(part)f(of)g Fq(h)p Fs(f)5 b(;)15 b(D)2260 3418 y Fo(Q)2320 3404 y Fs(g)s Fq(i)32 b Fz(is)e(not)h(0.)41 b(W)-8 b(e)31 b(no)m(w)g(let)874 3624 y Fs(\015)921 3638 y Fo(\017)979 3624 y Fz(=)25 b Fs(\017)1112 3586 y Fr(2)1166 3624 y Fz(\()q Fq(j)p Fs(f)10 b Fq(ih)p Fs(f)g Fq(j)20 b(\000)g(j)p Fs(g)s Fq(ih)p Fs(g)s Fq(j)p Fz(\))j(+)d Fs(\017)1941 3534 y Fp(p)p 2031 3534 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3220 y FA(1)1709 3247 y Fp(X)1708 3441 y Fo(n)p Fr(=1)1856 3333 y Fs(\013)1914 3296 y Fo(n)1961 3333 y Fs(\032)2008 3347 y Fo(n)2055 3333 y Fz(\()p Fs(Q;)g(\032)2249 3347 y Fo(Q)2310 3333 y Fz(\))p Fs(;)3618 3205 y Fz(\(25\))0 3586 y(where)30 b(w)m(e)h(recall)g(that)g Fs(Q)908 3600 y Fo(n)985 3586 y Fz(and)f Fs(\032)1209 3600 y Fo(n)1286 3586 y Fz(dep)s(end)e(on)j(b)s(oth)e Fs(Q)h Fz(and)g Fs(\032)2268 3600 y Fo(Q)2327 3586 y Fz(.)41 b(In)30 b(order)f(to)i(ha)m(v)m(e)h(a)e(b)s(etter)h(condition)0 3699 y(on)26 b Fs(\013)h Fz(and)f(\003,)i(w)m(e)f(shall)f(no)m(w)h(c)m (hange)g(the)g(second)g(equation)g(for)f(the)h(densit)m(y)-8 b(,)28 b(b)m(y)e(taking)i(in)m(to)f(accoun)m(t)h(the)0 3812 y(sp)s(ecial)j(form)f(of)g(the)h(\014rst)f(order)f(term)i Fs(\032)1461 3826 y Fr(1)1500 3812 y Fz(.)41 b(T)-8 b(o)31 b(this)f(end,)g(w)m(e)h(need)f(to)h(compute)g(this)f(term)h (explicitely)-8 b(.)0 4047 y Fe(The)35 b(\014rst)f(order)i(densit)m(y)0 4219 y Fz(Recall)c(that)1125 4364 y Fs(Q)1197 4378 y 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Fz(2)q Fq(j)-15 b(j)p Fs(Q)p Fq(j)g(j)2025 5683 y FA(Q)2107 5669 y Fz(+)20 b(2)2243 5599 y Fq(p)p 2319 5599 56 4 v 70 x Fs(\031)t Fq(j)-15 b(j)p Fs(\032)p Fq(j)g(j)2492 5683 y FA(C)2537 5669 y Fs(;)1844 5906 y Fz(17)p eop end %%Page: 18 18 TeXDict begin 18 17 bop 0 63 a Fz(where)30 b(w)m(e)h(recall)g(that)g Fs(C)901 77 y Fo(R)989 63 y Fz(is)g(de\014ned)e(in)h(Lemma)g(6.)141 176 y(W)-8 b(e)32 b(no)m(w)e(in)m(tro)s(duce)g(the)h(function)f Fs(F)38 b Fz(:)26 b Fq(X)38 b(!)25 b(X)44 b Fz(de\014ned)29 b(b)m(y)1223 405 y Fs(F)13 b Fz(\()p Fs(Q;)i(\032)p Fz(\))26 b(=)1645 277 y Fp(\022)1712 405 y Fs(F)1770 419 y Fo(Q)1830 405 y Fz(\()p Fs(Q;)15 b(\032)p Fz(\))31 b Fs(;)46 b(F)2219 419 y Fo(\032)2260 405 y Fz(\()p Fs(Q;)15 b(\032)p Fz(\))2489 277 y Fp(\023)0 634 y Fz(where)904 794 y Fs(F)962 808 y Fo(Q)1022 794 y Fz(\()p Fs(Q;)g(\032)p Fz(\))26 b(=)f Fs(\037)1430 812 y Fr(\()p FA(\0001)p Fr(;0\))1669 794 y Fz(\()p Fs(D)1779 808 y Fo(Q;\032)1895 794 y Fz(\))c Fq(\000)f Fs(P)2113 756 y Fr(0)2177 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3491 338 4 v 1378 3574 a Fz(1)21 b(+)f Fs(\013B)1662 3588 y Fr(\003)1726 3512 y Fz(2)1771 3442 y Fq(p)p 1847 3442 56 4 v 70 x Fs(\031)s(Z)7 b Fq(j)-15 b(j)p Fs(n)p Fq(j)g(j)2096 3526 y FA(C)2166 3512 y Fq(\024)2304 3450 y Fs(b)p 2272 3491 104 4 v 2272 3574 a Fz(2)p Fs(\013)2386 3512 y(:)141 3736 y Fz(The)38 b(\014rst)f(inequation)i(of)46 b(\(36\))40 b(is)e(simpler)g(when)f(it)i(is)f(written)g(in)g(terms)h(of)f(the)g(v) -5 b(ariables)39 b Fs(\013)g Fz(and)0 3849 y Fs(x)25 b Fz(:=)g Fs(\013R)q Fz(.)41 b(It)31 b(b)s(ecomes)858 3993 y Fs(b)p 825 4033 V 825 4117 a Fz(2)p Fs(\013)959 4054 y Fz(+)20 b Fs(\024)1102 4068 y Fr(1)1142 4054 y Fz(\(\003\))p Fs(b=)p Fz(2)i(+)e Fs(f)10 b Fz(\()p Fs(b=)p Fz(2\))21 b(+)f Fs(\024)1935 4068 y Fr(1)1975 4054 y Fz(\(\003\))p Fs(x)h Fz(+)f Fs(xf)2379 4017 y FA(0)2401 4054 y Fz(\()p Fs(x)h Fz(+)f Fs(b=)p Fz(2\))26 b Fq(\024)2899 3993 y Fs(x)p 2896 4033 59 4 v 2896 4117 a(\013)3618 4054 y Fz(\(37\))0 4265 y(whic)m(h)32 b(implies)g Fs(b=)p Fz(2)d Fq(\024)e 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5385 y Fs(=)-5 b(A)1090 5399 y Fr(\003)1174 5385 y Fz(and)1134 5620 y Fs(\013)1192 5635 y Fo(b)1227 5620 y Fz(\(\003\))26 b(:=)f(min)1674 5492 y Fp(\022)1741 5620 y Fs(A)1809 5635 y Fo(b)1843 5620 y Fz(\(\003\))p Fs(;)2255 5558 y Fz(1)p 2027 5599 501 4 v 2027 5692 a Fs(\031)s(=)p Fz(4)d(+)e Fs(R)2354 5706 y Fr(\003)2407 5617 y Fq(p)p 2482 5617 46 4 v 2482 5692 a Fz(2)2538 5492 y Fp(\023)2620 5620 y Fs(:)1844 5906 y Fz(19)p eop end %%Page: 20 20 TeXDict begin 20 19 bop 141 68 a Fz(As)30 b(a)h(conclusion,)g(for)f (all)h(0)25 b Fq(\024)g Fs(\013)h Fq(\024)f Fs(\013)1485 83 y Fo(b)1520 68 y Fz(\(\003\),)31 b(there)f(exists)h(some)g Fs(R)2489 82 y Fr(0)2553 68 y Fz(=)25 b Fs(R)2718 82 y Fr(0)2758 68 y Fz(\()p Fs(\013;)15 b Fz(\003)p Fs(;)g(b)p Fz(\))32 b(suc)m(h)e(that)g(\()p Fs(\013;)15 b(R)3703 82 y Fr(0)3744 68 y Fz(\))0 181 y(is)34 b(a)h(solution)f(of)41 b(\(35\))r(.)52 b(This)33 b(means)h(that)h Fs(F)47 b Fz(is)34 b(a)g(con)m(traction)j(on)c Fs(B)5 b Fz(\(0)p Fs(;)15 b(R)2722 195 y Fr(0)2763 181 y Fz(\),)35 b(on)f(whic)m(h)g(w)m (e)g(can)h(apply)0 294 y(Banac)m(h)23 b(Theorem.)37 b(This)21 b(giv)m(es)i(a)f(unique)e(solution)i(to)g(the)g(equation)g Fs(F)13 b Fz(\()p Fs(Q;)i(\032)p Fz(\))27 b(=)e(\()p Fs(Q;)15 b(\032)p Fz(\))22 b(in)f Fs(B)5 b Fz(\(0)p Fs(;)15 b(R)3479 308 y Fr(0)3520 294 y Fz(\))25 b Fq(\032)g(X)13 b Fz(.)141 407 y(Let)28 b(us)e(no)m(w)i(sho)m(w)f(that)g Fs(P)41 b Fz(is)27 b(indeed)g(a)g(solution)h(to)g(\(4\))q(.)40 b(In)26 b(fact)i Fs(\032)f Fz(is)h(a)f(solution)h(to)g(\(29\))h(and)d (so)i(it)f(is)0 520 y(a)32 b(solution)h(to)f(\(28\))r(.)45 b(On)31 b(the)h(other)g(hand,)f(w)m(e)i(ha)m(v)m(e)g Fs(Q)27 b Fz(=)g Fs(\037)2172 538 y Fr(\()p FA(\0001)p Fr(;0\))2412 520 y Fz(\()p Fs(D)2522 534 y Fo(Q;\032)2638 520 y Fz(\))21 b Fq(\000)g Fs(P)2857 487 y Fr(0)2897 520 y Fz(,)32 b(and)f(so)h(equation)h(\(28\))0 633 y(means)f(exactly)i (that)f Fs(\032)28 b Fz(=)g Fs(\032)1015 647 y Fo(Q)1075 633 y Fz(.)46 b(Hence,)34 b Fs(P)45 b Fz(is)32 b(a)h(solution)f(to)h Fs(P)42 b Fz(=)28 b Fs(\037)2432 651 y Fr(\()p FA(\0001)p Fr(;0\))2671 633 y Fz(\()p Fs(D)2781 647 y Fo(Q)2841 633 y Fz(\).)47 b(Thanks)31 b(to)i(the)f(pro)s(of,)0 746 y(w)m(e)f(kno)m(w)f(that)h Fs(P)43 b Fz(satis\014es)31 b(the)g(assumptions)f(of)g(Theorem)g(3,)h(and)f(so)h Fs(P)43 b Fz(is)30 b(a)h Fs(B)5 b(D)s(F)13 b Fz(-stable)31 b(v)-5 b(acuum.)141 904 y(T)d(o)32 b(end)e(the)i(pro)s(of,)f(let)h(us)f (study)f(the)i(b)s(eha)m(viour)e(of)i Fs(A)2124 919 y Fo(b)2158 904 y Fz(\(\003\))g(as)g(\003)27 b Fq(!)f(1)p Fz(.)44 b(Di\013eren)m(tiating)35 b(\(38\))e(with)0 1017 y(resp)s(ect)d(to)h Fs(x)p Fz(,)g(w)m(e)g(arriv)m(e)g(at)697 1252 y Fs(\024)749 1266 y Fr(1)789 1252 y Fz(\(\003\))p Fs(b)21 b Fz(+)f Fs(f)10 b Fz(\()p Fs(b)p Fz(\))20 b(+)1358 1190 y Fs(bf)1452 1157 y FA(0)1474 1190 y Fz(\()p Fs(x)1561 1204 y Fr(\003)1635 1190 y Fz(+)g Fs(b=)p Fz(2\))p 1358 1231 534 4 v 1602 1314 a(2)1926 1252 y(=)25 b(\()p Fs(x)2109 1266 y Fr(\003)2183 1252 y Fq(\000)20 b Fs(b=)p Fz(2\))p Fs(x)2490 1266 y Fr(\003)2544 1252 y Fs(f)2599 1214 y FA(00)2641 1252 y Fz(\()p Fs(x)2728 1266 y Fr(\003)2801 1252 y Fz(+)g Fs(b=)p Fz(2\))p Fs(:)537 b Fz(\(40\))0 1468 y(Since)34 b Fs(\024)293 1482 y Fr(1)332 1468 y Fz(\(\003\))e Fq(!)e(1)k Fz(as)f(\003)e Fq(!)f(1)p Fz(,)35 b(w)m(e)f(deduce)f(that)h Fs(x)1918 1482 y Fr(\003)1993 1468 y Fz(+)22 b Fs(b=)p Fz(2)32 b Fq(!)e Fz(1,)35 b(or)f(equiv)-5 b(alen)m(tly)35 b Fs(x)3148 1482 y Fr(\003)3232 1468 y Fq(!)30 b Fz(1)23 b Fq(\000)f Fs(b=)p Fz(2.)51 b(If)0 1581 y(w)m(e)36 b(no)m(w)g(use)g(the)g(fact)g(that)h Fs(f)1101 1548 y FA(0)1123 1581 y Fz(\()p Fs(y)s Fz(\))e(=)f Fs(o)1425 1507 y Fp(\000)1467 1581 y Fs(f)1522 1548 y FA(00)1564 1581 y Fz(\()p Fs(y)s Fz(\))1682 1507 y Fp(\001)1760 1581 y Fz(as)i Fs(y)h Fq(!)d Fz(1)2129 1548 y FA(\000)2189 1581 y Fz(,)j(w)m(e)f(\014nally)g(obtain)g Fs(f)3014 1548 y FA(00)3056 1581 y Fz(\()p Fs(x)3143 1595 y Fr(\003)3220 1581 y Fz(+)24 b Fs(b=)p Fz(2\))36 b Fq(\030)3586 1595 y Fr(\003)p FA(!1)116 1671 y Fo(b\024)187 1680 y Fi(1)221 1671 y Fr(\(\003\))p 10 1695 422 4 v 10 1748 a(\(1)p FA(\000)p Fo(b)p Fr(\)\(1)p FA(\000)p Fo(b=)p Fr(2\))471 1716 y Fz(and)30 b Fs(f)703 1683 y FA(0)726 1716 y Fz(\()p Fs(x)813 1730 y Fr(\003)886 1716 y Fz(+)20 b Fs(b=)p Fz(2\))27 b(=)e Fs(o)1308 1642 y Fp(\000)1349 1716 y Fs(\024)1401 1730 y Fr(1)1441 1716 y Fz(\(\003\))1574 1642 y Fp(\001)1617 1716 y Fz(.)40 b(By)32 b(\(38\))r(,)e(this)h (implies)1536 1975 y Fs(A)1604 1989 y Fr(\003)1683 1975 y Fq(\030)1754 1989 y Fr(\003)p FA(!1)1998 1914 y Fz(1)20 b Fq(\000)g Fs(b)p 1983 1954 226 4 v 1983 2038 a(\024)2035 2052 y Fr(1)2074 2038 y Fz(\(\003\))2218 1975 y Fs(:)0 2241 y Fz(Remark)30 b(also)i(that)f Fs(R)791 2255 y Fr(\003)869 2241 y Fz(=)25 b Fs(x)1017 2255 y Fr(\003)1070 2241 y Fs(=)-5 b(A)1178 2255 y Fr(\003)1257 2241 y Fq(\030)1363 2196 y Fr(1)p FA(\000)p Fo(b=)p Fr(2)p 1363 2220 191 4 v 1398 2272 a(1)p FA(\000)p Fo(b)1564 2241 y Fs(\024)1616 2255 y Fr(1)1656 2241 y Fz(\(\003\),)31 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5360 y Fs(;)647 5653 y Fq(j)g(j)p Fs(Q)754 5667 y Fr(1)p Fo(;)p Fr(0)849 5653 y Fq(j)g(j)884 5667 y FA(Q)971 5653 y Fq(\024)25 b(j)-15 b(j)p Fs(R)1171 5667 y Fo(Q)1231 5653 y Fq(j)g(j)1266 5667 y FA(R)1356 5653 y Fq(\024)25 b Fs(C)1517 5667 y Fo(R)1575 5653 y Fq(j)-15 b(j)p Fs(Q)p Fq(j)g(j)1717 5667 y FA(Q)1779 5653 y Fs(;)201 b Fq(j)-15 b(j)p Fs(\032)2087 5667 y Fr(1)p Fo(;)p Fr(0)2182 5653 y Fq(j)g(j)2217 5667 y FA(C)2288 5653 y Fq(\024)2394 5591 y Fs(C)2459 5605 y Fo(R)2516 5591 y Fz(\(log)18 b(\003\))2782 5558 y Fr(1)p Fo(=)p Fr(2)p 2394 5632 500 4 v 2593 5715 a Fz(4)p Fs(\031)2903 5653 y Fq(j)-15 b(j)p Fs(Q)p Fq(j)g(j)3045 5667 y FA(Q)3107 5653 y Fs(:)1844 5906 y Fz(20)p eop end %%Page: 21 21 TeXDict begin 21 20 bop 0 63 a Fy(Ther)-5 b(efor)g(e)599 176 y Fq(j)-14 b(j)p Fz(\()p Fs(Q)742 190 y Fr(1)781 176 y Fs(;)15 b(\032)868 190 y Fr(1)p Fo(;)p Fr(0)963 176 y Fz(\))p Fq(j)-14 b(j)25 b(\024)g Fs(\024)1207 190 y Fr(1)1247 176 y Fz(\(\003\))1395 99 y Fp(\014)1395 153 y(\014)1411 99 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Fr(\))1516 1268 y Fy(and)32 b Fz(\003)1754 1235 y FA(\000)1813 1268 y Fz(\()p Fs(p)p Fz(\))26 b(=)2061 1223 y FA(\000)p Fr(\()p Fc(\013)p FA(\001)p Fo(p)p Fr(+)p Fo(\014)s Fr(\)+)p Fo(E)t Fr(\()p Fo(p)p Fr(\))p 2061 1247 518 4 v 2229 1300 a(2)p Fo(E)t Fr(\()p Fo(p)p Fr(\))2619 1268 y Fy(b)-5 b(e)31 b(the)h(pr)-5 b(oje)g(ctions)33 b(matric)-5 b(es)33 b(in)0 1401 y Fm(C)66 1368 y Fr(4)138 1401 y Fy(onto)g(the)g(eigensp)-5 b(ac)g(es)34 b(of)f Fs(D)1159 1368 y Fr(0)1231 1401 y Fy(in)f(F)-7 b(ourier)34 b(sp)-5 b(ac)g(e.)43 b(We)32 b(then)h(have)858 1607 y Fz(T)-8 b(r)952 1626 y Fj(C)1000 1608 y Fi(4)1054 1607 y Fz(\()p Fs(M)10 b Fz(\()p Fs(p;)15 b(q)s Fz(\)\))26 b(=)f Fq(\000)p Fz(4)1891 1545 y(1)p 1670 1586 487 4 v 1670 1669 a Fs(E)5 b Fz(\()p Fs(p)p Fz(\))21 b(+)f Fs(E)5 b Fz(\()p Fs(q)s Fz(\))2167 1607 y(T)-8 b(r)2261 1626 y Fj(C)2309 1608 y Fi(4)2363 1533 y Fp(\000)2404 1607 y Fz(\003)2467 1569 y Fr(+)2527 1607 y Fz(\()p Fs(p)p Fz(\)\003)2706 1569 y FA(\000)2765 1607 y Fz(\()p Fs(q)s Fz(\))2879 1533 y Fp(\001)414 1880 y Fq(j)p Fs(M)10 b Fz(\()p Fs(p;)15 b(q)s Fz(\))p Fq(j)762 1842 y Fr(2)828 1880 y Fz(=)25 b(T)-8 b(r)1018 1900 y Fj(C)1066 1881 y Fi(4)1120 1880 y Fz(\()p Fs(M)10 b Fz(\()p Fs(p;)15 b(q)s Fz(\))p Fs(M)10 b Fz(\()p Fs(p;)15 b(q)s Fz(\))1751 1842 y FA(\003)1792 1880 y Fz(\))26 b(=)f(8)2280 1818 y(1)p 2004 1859 597 4 v 2004 1942 a(\()p Fs(E)5 b Fz(\()p Fs(p)p Fz(\))21 b(+)f Fs(E)5 b Fz(\()p Fs(q)s Fz(\)\))2560 1916 y Fr(2)2611 1880 y Fz(T)-8 b(r)2705 1900 y Fj(C)2753 1881 y Fi(4)2807 1806 y Fp(\000)2848 1880 y Fz(\003)2911 1842 y Fr(+)2970 1880 y Fz(\()p Fs(p)p Fz(\)\003)3149 1842 y FA(\000)3209 1880 y Fz(\()p Fs(q)s Fz(\))3323 1806 y Fp(\001)726 2131 y Fz(T)g(r)819 2151 y Fj(C)867 2132 y Fi(4)921 2058 y Fp(\000)963 2131 y Fz(\003)1026 2094 y Fr(+)1085 2131 y Fz(\()p Fs(p)p Fz(\)\003)1264 2094 y FA(\000)1324 2131 y Fz(\()p Fs(q)s Fz(\))1438 2058 y Fp(\001)1505 2131 y Fz(=)25 b(T)-8 b(r)1695 2151 y Fj(C)1743 2132 y Fi(4)1797 2058 y Fp(\000)1838 2131 y Fz(\003)1901 2094 y FA(\000)1960 2131 y Fz(\()p Fs(p)p Fz(\)\003)2139 2094 y Fr(+)2199 2131 y Fz(\()p Fs(q)s Fz(\))2313 2058 y Fp(\001)2381 2131 y Fz(=)24 b(1)d Fq(\000)2675 2070 y Fs(p)f Fq(\001)g Fs(q)j Fz(+)d(1)p 2643 2111 376 4 v 2643 2194 a Fs(E)5 b Fz(\()p Fs(p)p Fz(\))p Fs(E)g Fz(\()p Fs(q)s Fz(\))3029 2131 y Fs(:)0 2326 y Fy(Mor)-5 b(e)g(over,)34 b(we)e(have)641 2549 y Fq(8)p Fs(p;)15 b(q)28 b Fq(2)d Fm(R)999 2511 y Fr(3)1038 2549 y Fs(;)113 b Fz(T)-8 b(r)1269 2569 y Fj(C)1317 2550 y Fi(4)1371 2475 y Fp(\000)1413 2549 y Fz(\003)1476 2511 y Fr(+)1535 2549 y Fz(\()p Fs(p)p Fz(\)\003)1714 2511 y FA(\000)1774 2549 y Fz(\()p Fs(q)s Fz(\))1888 2475 y Fp(\001)1955 2549 y Fq(\024)25 b Fz(min)2218 2421 y Fp(\022)2445 2487 y Fq(j)p Fs(p)20 b Fq(\000)g Fs(q)s Fq(j)2696 2454 y Fr(2)p 2295 2528 591 4 v 2295 2611 a Fz(2)p Fs(E)5 b Fz(\(\()p Fs(p)21 b Fz(+)f Fs(q)s Fz(\))p Fs(=)p Fz(2\))2844 2585 y Fr(2)2910 2549 y Fs(;)2976 2487 y Fz(1)p 2976 2528 46 4 v 2976 2611 a(2)3031 2421 y Fp(\023)3113 2549 y Fs(:)480 b Fz(\(42\))141 2776 y Fy(Pr)-5 b(o)g(of)33 b(of)f(L)-5 b(emma)32 b(10)h({)60 b Fz(W)-8 b(e)31 b(only)e(pro)m(v)m (e)h(\(42\).)42 b(W)-8 b(e)30 b(ha)m(v)m(e)g(T)-8 b(r)2323 2796 y Fj(C)2371 2777 y Fi(4)2425 2776 y Fz(\(\003)2523 2743 y Fr(+)2582 2776 y Fz(\()p Fs(p)p Fz(\)\003)2761 2743 y FA(\000)2821 2776 y Fz(\()p Fs(q)s Fz(\)\))26 b Fq(\024)f(j)p Fz(\003)3180 2743 y Fr(+)3239 2776 y Fz(\()p Fs(p)p Fz(\))p Fq(j)15 b(j)p Fz(\003)3483 2743 y FA(\000)3544 2776 y Fz(\()p Fs(q)s Fz(\))p Fq(j)26 b Fz(=)0 2908 y(1)p Fs(=)p Fz(2,)32 b(so)f(when)e Fs(t)c Fz(:=)846 2863 y FA(j)p Fo(p)p FA(\000)p Fo(q)r FA(j)1011 2840 y Fi(2)p 730 2887 430 4 v 730 2941 a Fr(4)p Fo(E)t Fr(\(\()p Fo(p)p Fr(+)p Fo(q)r Fr(\))p Fo(=)p Fr(2\))1124 2923 y Fi(2)1195 2908 y Fq(\025)g Fz(1)p Fs(=)p Fz(2,)32 b(there)f(is)f(nothing)h(to)g(pro)m(v)m(e.)41 b(No)m(w)31 b(w)m(e)g(ha)m(v)m(e)538 3163 y(1)21 b Fq(\000)737 3102 y Fs(p)f Fq(\001)g Fs(q)j Fz(+)d(1)p 705 3142 376 4 v 705 3226 a Fs(E)5 b Fz(\()p Fs(p)p Fz(\))p Fs(E)g Fz(\()p Fs(q)s Fz(\))1174 3163 y(=)82 b(1)21 b Fq(\000)1614 3102 y Fs(l)1643 3069 y Fr(2)1703 3102 y Fq(\000)f Fs(k)1844 3069 y Fr(2)1904 3102 y Fz(+)f(1)p 1494 3142 667 4 v 1494 3226 a Fs(E)5 b Fz(\()p Fs(l)23 b Fz(+)d Fs(k)s Fz(\))p Fs(E)5 b Fz(\()p Fs(l)23 b Fq(\000)d Fs(k)s Fz(\))2201 3163 y(with)30 b Fs(l)d Fz(=)2568 3102 y Fs(p)20 b Fz(+)g Fs(q)p 2568 3142 201 4 v 2645 3226 a Fz(2)2778 3163 y Fs(;)46 b(k)29 b Fz(=)3031 3102 y Fs(p)19 b Fq(\000)h Fs(q)p 3031 3142 V 3108 3226 a Fz(2)1174 3402 y(=)82 b(1)21 b Fq(\000)1712 3340 y Fz(1)g Fq(\000)f Fs(t)p 1494 3381 627 4 v 1494 3399 a Fp(p)p 1585 3399 536 4 v 78 x Fz(\(1)h(+)f Fs(t)p Fz(\))1845 3451 y Fr(2)1904 3477 y Fq(\000)g Fz(4)p Fs(z)t(t)0 3673 y Fz(where)31 b Fs(t)26 b Fz(=)g Fq(j)p Fs(k)s Fq(j)520 3640 y Fr(2)560 3673 y Fs(=E)5 b Fz(\()p Fs(l)r Fz(\))776 3640 y Fr(2)848 3673 y Fz(and)31 b Fs(z)f Fz(=)1278 3628 y Fr(\()p Fo(l)q FA(\001)p Fo(k)r Fr(\))1413 3604 y Fi(2)p 1205 3652 314 4 v 1205 3706 a FA(j)p Fo(k)r FA(j)1284 3687 y Fi(2)1318 3706 y Fr(\(1+)p Fo(l)1457 3687 y Fi(2)1492 3706 y Fr(\))1556 3673 y Fq(2)c Fz([0;)15 b(1\).)45 b(When)30 b Fs(t)d Fq(2)f Fz([0;)15 b(1)p Fs(=)p Fz(2\))34 b(and)c Fs(z)h Fq(2)26 b Fz([0;)15 b(1\),)33 b(the)f(expression)0 3794 y(ab)s(o)m(v)m(e)g(is)e(decreasing)h(in)f Fs(z)35 b Fz(and)30 b(so)g(w)m(e)h(obtain)1005 4000 y(1)20 b Fq(\000)1203 3939 y Fs(p)g Fq(\001)g Fs(q)j Fz(+)d(1)p 1171 3979 376 4 v 1171 4062 a Fs(E)5 b Fz(\()p Fs(p)p Fz(\))p Fs(E)g Fz(\()p Fs(q)s Fz(\))1582 4000 y Fq(\024)25 b Fz(1)c Fq(\000)1945 3939 y Fz(1)g Fq(\000)f Fs(t)p 1845 3979 391 4 v 1845 3997 a Fp(p)p 1935 3997 300 4 v 1935 4076 a Fz(\(1)h(+)f Fs(t)p Fz(\))2195 4049 y Fr(2)2270 4000 y Fz(=)2432 3939 y(2)p Fs(t)p 2376 3979 190 4 v 2376 4062 a Fz(1)h(+)f Fs(t)2601 4000 y Fq(\024)25 b Fz(2)p Fs(t)0 4234 y Fz(whic)m(h)30 b(ends)g(the)g(pro)s(of.)p 3714 4234 4 62 v 3718 4176 55 4 v 3718 4234 V 3771 4234 4 62 v 0 4425 a Fq(\017)h Fz(Let)g(us)e(no)m(w)i(treat)g Fs(Q)839 4439 y Fr(0)p Fo(;)p Fr(1)933 4425 y Fz(.)41 b(F)-8 b(rom)31 b(\(41\))r(,)f(w)m(e)h(obtain)1072 4640 y Fq(j)1115 4617 y Fp(d)1097 4640 y Fs(Q)1169 4654 y Fr(0)p Fo(;)p Fr(1)1263 4640 y Fz(\()p Fs(p;)15 b(q)s Fz(\))p Fq(j)1488 4602 y Fr(2)1554 4640 y Fz(=)1727 4578 y(1)p 1660 4619 180 4 v 1660 4702 a(2)1705 4676 y Fr(5)1745 4702 y Fs(\031)1800 4676 y Fr(3)1849 4640 y Fq(j)1891 4616 y Fp(b)1874 4640 y Fs(')1933 4614 y FA(0)1957 4640 y Fq(j)1982 4602 y Fr(2)2022 4640 y Fz(\()p Fs(p)20 b Fq(\000)g Fs(q)s Fz(\))p Fq(j)p Fs(M)10 b Fz(\()p Fs(p;)15 b(q)s Fz(\))p Fq(j)2641 4602 y Fr(2)2682 4640 y Fs(;)0 4833 y Fz(and)30 b(so)98 4926 y Fp(Z)10 b(Z)265 5050 y Fs(E)5 b Fz(\()p Fs(p)20 b Fq(\000)g Fs(q)s Fz(\))608 5012 y Fr(2)648 5050 y Fs(E)5 b Fz(\()p Fs(p)21 b Fz(+)f Fs(q)s Fz(\))p Fq(j)1034 5027 y Fp(d)1017 5050 y Fs(Q)1089 5064 y Fr(0)p Fo(;)p Fr(1)1183 5050 y Fz(\()p Fs(p;)15 b(q)s Fz(\))p Fq(j)1408 5012 y Fr(2)1449 5050 y Fs(dp)g(dq)506 5285 y Fz(=)679 5224 y(1)p 612 5264 V 612 5347 a(2)657 5321 y Fr(5)697 5347 y Fs(\031)752 5321 y Fr(3)816 5161 y Fp(Z)10 b(Z)998 5285 y Fs(dk)19 b(duE)5 b Fz(\()p Fs(k)s Fz(\))1402 5248 y Fr(2)1443 5285 y Fs(E)g Fz(\(2)p Fs(u)p Fz(\))p Fq(j)1725 5261 y Fp(b)1707 5285 y Fs(')1766 5259 y FA(0)1791 5285 y Fq(j)1816 5248 y Fr(2)1856 5285 y Fz(\()p Fs(k)s Fz(\))p Fs(\037)p Fz(\()p Fq(j)p Fs(u)p Fq(j)27 b(\024)e Fz(\003\))p Fq(j)p Fs(M)10 b Fz(\()p Fs(u)21 b Fz(+)f Fs(k)s(=)p Fz(2)p Fs(;)15 b(u)22 b Fq(\000)e Fs(k)s(=)p Fz(2\))p Fq(j)3258 5248 y Fr(2)1474 5556 y Fq(\024)1647 5494 y Fz(4)p 1580 5535 V 1580 5618 a(2)1625 5592 y Fr(5)1665 5618 y Fs(\031)1720 5592 y Fr(3)1785 5427 y Fp(\022)1852 5432 y(Z)1958 5556 y Fs(dk)s Fq(j)p Fs(k)s Fq(j)2155 5518 y Fr(2)2196 5556 y Fs(E)5 b Fz(\()p Fs(k)s Fz(\))2388 5518 y Fr(2)2428 5556 y Fq(j)2470 5532 y Fp(b)2453 5556 y Fs(')2512 5529 y FA(0)2536 5556 y Fq(j)2561 5518 y Fr(2)2601 5556 y Fz(\()p Fs(k)s Fz(\))2721 5427 y Fp(\023)2804 5400 y( )2876 5432 y(Z)2926 5638 y FA(j)p Fo(u)p FA(j\024)p Fr(\003)3354 5494 y Fz(1)p 3139 5535 476 4 v 3139 5618 a Fs(E)g Fz(\(2)p Fs(u)p Fz(\))p Fs(E)g Fz(\()p Fs(u)p Fz(\))3572 5592 y Fr(2)3625 5400 y Fp(!)1844 5906 y Fz(21)p eop end %%Page: 22 22 TeXDict begin 22 21 bop 0 63 a Fz(b)m(y)30 b(Lemma)h(10.)41 b(No)m(w)31 b(w)m(e)g(ha)m(v)m(e)342 245 y Fp(Z)393 451 y FA(j)p Fo(u)p FA(j\024)p Fr(\003)794 307 y Fs(du)p 606 348 476 4 v 606 431 a(E)5 b Fz(\(2)p Fs(u)p Fz(\))p Fs(E)g Fz(\()p Fs(u)p Fz(\))1039 405 y Fr(2)1116 369 y Fz(=)25 b(4)p Fs(\031)1328 213 y Fp( )1410 307 y Fz(1)p 1410 348 46 4 v 1410 431 a(2)1465 369 y(argsh\(2\003\))d(+)2016 307 y(1)p 1978 348 122 4 v 1978 366 a Fq(p)p 2054 366 46 4 v 75 x Fz(3)2110 369 y(argth)2337 213 y Fp( )2543 232 y Fq(p)p 2619 232 V 75 x Fz(3\003)p 2419 348 432 4 v 2419 366 a Fp(p)p 2510 366 341 4 v 92 x Fz(1)f(+)e(4)2711 381 y Fq(p)p 2788 381 64 4 v 2788 458 a Fz(\003)2861 213 y Fp(!!)3030 369 y Fq(\024)25 b Fz(2)p Fs(\031)19 b Fz(log)e(\003)181 b(\(43\))0 674 y(for)30 b(\003)c Fq(\025)e Fz(3.)42 b(So)30 b(w)m(e)h(obtain)999 959 y Fq(j)-15 b(j)p Fs(Q)1106 973 y Fr(0)p Fo(;)p Fr(1)1201 959 y Fq(j)g(j)1236 973 y FA(Q)1323 959 y Fq(\024)1429 898 y Fz(\(log)18 b(\003\))1695 865 y Fr(1)p Fo(=)p Fr(2)p 1429 938 377 4 v 1567 1022 a Fz(2)p Fs(\031)1816 959 y Fq(j)-15 b(j)p Fs(')1910 922 y FA(0)1934 959 y Fq(j)g(j)1969 973 y FA(Y)2051 959 y Fz(=)25 b(2\(log)18 b(\003\))2458 922 y Fr(1)p Fo(=)p Fr(2)2569 959 y Fq(j)-15 b(j)p Fs(\032)2651 922 y FA(0)2674 959 y Fq(j)g(j)2709 973 y FA(C)2755 959 y Fs(:)0 1361 y Fq(\017)31 b Fs(\032)123 1375 y Fr(1)p Fo(;)p Fr(0)247 1361 y Fz(and)f Fs(Q)496 1375 y Fr(1)p Fo(;)p Fr(0)590 1361 y Fz(.)141 1484 y(W)-8 b(e)32 b(ha)m(v)m(e)1114 1659 y Fs(Q)1186 1673 y Fr(1)p Fo(;)p Fr(0)1306 1659 y Fz(=)25 b Fq(\000)1510 1597 y Fz(1)p 1483 1638 101 4 v 1483 1721 a(2)p Fs(\031)1608 1535 y Fp(Z)1699 1561 y Fr(+)p FA(1)1659 1741 y(\0001)1844 1659 y Fs(d\021)2081 1597 y Fz(1)p 1949 1638 309 4 v 1949 1721 a Fs(D)2027 1695 y Fr(0)2087 1721 y Fz(+)20 b Fs(i\021)2267 1659 y(R)2478 1597 y Fz(1)p 2347 1638 V 2347 1721 a Fs(D)2425 1695 y Fr(0)2485 1721 y Fz(+)f Fs(i\021)0 1908 y Fz(so)31 b(that)446 2151 y Fp(d)429 2174 y Fs(Q)501 2188 y Fr(1)p Fo(;)p Fr(0)595 2174 y Fz(\()p Fs(p;)15 b(q)s Fz(\))83 b(=)g Fq(\000)p Fz(\(2)p Fs(\031)s Fz(\))1273 2136 y FA(\000)p Fr(1)1384 2050 y Fp(Z)1474 2076 y Fr(+)p FA(1)1434 2256 y(\0001)1619 2174 y Fs(d\021)1972 2112 y Fz(1)p 1724 2153 539 4 v 1724 2236 a Fn(\013)21 b Fq(\001)g Fs(p)f Fz(+)g Fs(\014)25 b Fz(+)20 b Fs(i\021)2291 2151 y Fp(b)2274 2174 y Fs(R)p Fz(\()p Fs(p;)15 b(q)s Fz(\))2800 2112 y(1)p 2553 2153 537 4 v 2553 2236 a Fn(\013)21 b Fq(\001)g Fs(q)i Fz(+)d Fs(\014)25 b Fz(+)20 b Fs(i\021)878 2428 y Fz(=)83 b Fq(\000)1113 2367 y Fz(1)p 1113 2407 46 4 v 1113 2490 a(2)1399 2367 y(1)p 1178 2407 487 4 v 1178 2490 a Fs(E)5 b Fz(\()p Fs(p)p Fz(\))21 b(+)f Fs(E)5 b Fz(\()p Fs(q)s Fz(\))1690 2300 y Fp(\022)1767 2367 y Fz(\()p Fn(\013)21 b Fq(\001)f Fs(p)g Fz(+)g Fs(\014)5 b Fz(\))p 1767 2407 419 4 v 1882 2490 a Fs(E)g Fz(\()p Fs(p)p Fz(\))2213 2405 y Fp(b)2196 2428 y Fs(R)p Fz(\()p Fs(p;)15 b(q)s Fz(\))2475 2367 y(\()p Fn(\013)22 b Fq(\001)e Fs(q)j Fz(+)d Fs(\014)5 b Fz(\))p 2475 2407 417 4 v 2591 2490 a Fs(E)g Fz(\()p Fs(q)s Fz(\))2923 2428 y Fq(\000)3031 2405 y Fp(b)3014 2428 y Fs(R)p Fz(\()p Fs(p;)15 b(q)s Fz(\))3283 2300 y Fp(\023)0 2706 y Fz(and)657 2864 y Fq(j)700 2841 y Fp(d)682 2864 y Fs(Q)754 2878 y Fr(1)p Fo(;)p Fr(0)849 2864 y Fz(\()p Fs(p;)g(q)s Fz(\))p Fq(j)1074 2826 y Fr(2)1139 2864 y Fq(\024)1521 2802 y Fz(1)p 1245 2843 597 4 v 1245 2926 a(\()p Fs(E)5 b Fz(\()p Fs(p)p Fz(\))22 b(+)d Fs(E)5 b Fz(\()p Fs(q)s Fz(\)\))1801 2900 y Fr(2)1852 2864 y Fq(j)1895 2841 y Fp(b)1877 2864 y Fs(R)q Fz(\()p Fs(p;)15 b(q)s Fz(\))p Fq(j)2172 2826 y Fr(2)2238 2864 y Fq(\024)2512 2802 y Fz(1)p 2344 2843 384 4 v 2344 2926 a Fs(E)5 b Fz(\()p Fs(p)20 b Fz(+)g Fs(q)s Fz(\))2687 2900 y Fr(2)2737 2864 y Fq(j)2779 2841 y Fp(b)2762 2864 y Fs(R)q Fz(\()p Fs(p;)15 b(q)s Fz(\))p Fq(j)3057 2826 y Fr(2)3097 2864 y Fs(;)0 3108 y Fz(sho)m(wing)30 b(that)1341 3250 y Fq(j)-15 b(j)p Fs(Q)1448 3264 y Fr(1)p Fo(;)p Fr(0)1542 3250 y Fq(j)g(j)1577 3264 y FA(Q)1665 3250 y Fq(\024)25 b(j)-15 b(j)p Fs(R)q Fq(j)g(j)1901 3264 y FA(R)1991 3250 y Fq(\024)25 b Fs(C)2152 3264 y Fo(R)2209 3250 y Fq(j)-15 b(j)p Fs(Q)p Fq(j)g(j)2351 3264 y FA(Q)2414 3250 y Fs(:)0 3451 y Fz(No)m(w,)31 b(w)m(e)g(ha)m(v)m (e)244 3729 y Fp(d)-136 b Fs(\032)286 3743 y Fr(1)p Fo(;)p Fr(0)380 3729 y Fz(\()p Fs(k)s Fz(\))84 b(=)865 3667 y(1)p 748 3708 282 4 v 748 3795 a(\(2)p Fs(\031)s Fz(\))918 3769 y Fr(3)p Fo(=)p Fr(2)1054 3605 y Fp(Z)1104 3811 y Fj(R)1152 3792 y Fi(3)1206 3729 y Fz(T)-8 b(r)1300 3749 y Fj(C)1348 3730 y Fi(4)1402 3601 y Fp(\022)1486 3706 y(d)1469 3729 y Fs(Q)1541 3743 y Fr(1)p Fo(;)p Fr(0)1650 3601 y Fp(\022)1717 3729 y Fs(l)22 b Fz(+)1867 3667 y Fs(k)p 1867 3708 51 4 v 1869 3791 a Fz(2)1927 3729 y Fs(;)15 b(l)23 b Fq(\000)2118 3667 y Fs(k)p 2118 3708 V 2120 3791 a Fz(2)2178 3601 y Fp(\023\023)2312 3729 y Fs(dl)584 3983 y Fz(=)83 b Fq(\000)956 3921 y Fz(1)p 819 3962 321 4 v 819 4049 a(2)864 4023 y Fr(5)p Fo(=)p Fr(2)974 4049 y Fs(\031)1029 4023 y Fr(3)p Fo(=)p Fr(2)1164 3859 y Fp(Z)1214 4065 y Fj(R)1262 4046 y Fi(3)1316 3983 y Fz(T)-8 b(r)1410 4003 y Fj(C)1458 3984 y Fi(4)1512 3855 y Fp(\022)1596 3960 y(b)1579 3983 y Fs(R)1664 3855 y Fp(\022)1731 3983 y Fs(l)22 b Fz(+)1881 3921 y Fs(k)p 1881 3962 51 4 v 1883 4045 a Fz(2)1941 3983 y Fs(;)15 b(l)22 b Fq(\000)2131 3921 y Fs(k)p 2131 3962 V 2133 4045 a Fz(2)2191 3855 y Fp(\023)2273 3983 y Fs(M)2387 3855 y Fp(\022)2454 3983 y Fs(l)g Fz(+)2604 3921 y Fs(k)p 2604 3962 V 2606 4045 a Fz(2)2664 3983 y Fs(;)15 b(l)22 b Fq(\000)2854 3921 y Fs(k)p 2854 3962 V 2856 4045 a Fz(2)2914 3855 y Fp(\023\023)3048 3983 y Fs(\037)p Fz(\()p Fq(j)p Fs(l)r Fq(j)k(\024)f Fz(\003\))p Fs(dl)r(;)0 4261 y Fz(so)31 b(w)m(e)f(obtain)0 4545 y Fq(j)5 b Fp(d)-136 b Fs(\032)72 4559 y Fr(1)p Fo(;)p Fr(0)167 4545 y Fz(\()p Fs(k)s Fz(\))p Fq(j)26 b(\024)581 4483 y Fz(1)p 444 4524 321 4 v 444 4611 a(2)489 4585 y Fr(5)p Fo(=)p Fr(2)599 4611 y Fs(\031)654 4585 y Fr(3)p Fo(=)p Fr(2)790 4417 y Fp(\022)856 4421 y(Z)907 4627 y Fj(R)955 4608 y Fi(3)1009 4545 y Fs(E)5 b Fz(\(2)p Fs(l)r Fz(\))1225 4507 y FA(\000)p Fr(1)1321 4545 y Fq(j)1363 4522 y Fp(b)1346 4545 y Fs(R)q Fz(\()p Fs(l)22 b Fz(+)e Fs(k)s(=)p Fz(2)p Fs(;)15 b(l)24 b Fq(\000)19 b Fs(k)s(=)p Fz(2\))p Fq(j)2112 4507 y Fr(2)2169 4545 y Fs(dl)2245 4417 y Fp(\023)2312 4439 y Fr(1)p Fo(=)p Fr(2)2437 4417 y Fp(\022)2504 4421 y(Z)2555 4627 y Fj(R)2603 4608 y Fi(3)2656 4545 y Fs(E)5 b Fz(\(2)p Fs(l)r Fz(\))p Fq(j)p Fs(M)10 b Fz(\()p Fs(l)25 b Fz(+)20 b Fs(k)s(=)p Fz(2)p Fs(;)15 b(l)23 b Fq(\000)d Fs(k)s(=)p Fz(2\))p Fq(j)3694 4507 y Fr(2)3750 4545 y Fs(dl)3826 4417 y Fp(\023)3894 4439 y Fr(1)p Fo(=)p Fr(2)0 4823 y Fz(and)30 b(\014nally)550 4983 y Fp(Z)666 5045 y Fs(E)5 b Fz(\()p Fs(k)s Fz(\))858 5012 y Fr(2)p 666 5086 233 4 v 712 5169 a Fq(j)p Fs(k)s Fq(j)812 5143 y Fr(2)908 5107 y Fq(j)g Fp(d)-136 b Fs(\032)980 5121 y Fr(1)p Fo(;)p Fr(0)1075 5107 y Fz(\()p Fs(k)s Fz(\))p Fq(j)1220 5069 y Fr(2)1275 5107 y Fs(dk)29 b Fq(\024)1571 5045 y Fz(1)p 1504 5086 180 4 v 1504 5169 a(2)1549 5143 y Fr(5)1589 5169 y Fs(\031)1644 5143 y Fr(3)1694 5107 y Fq(j)-15 b(j)p Fs(R)q Fq(j)g(j)1834 5069 y Fr(2)1834 5129 y FA(R)1914 4983 y Fp(Z)1964 5189 y FA(j)p Fo(l)q FA(j\024)p Fr(\003)2350 5045 y Fz(1)p 2158 5086 429 4 v 2158 5169 a Fs(E)5 b Fz(\(2)p Fs(l)r Fz(\))p Fs(E)g Fz(\()p Fs(l)r Fz(\))2545 5143 y Fr(2)2612 5107 y Fs(dl)28 b Fq(\024)2820 5045 y Fz(log)17 b(\003)p 2820 5086 196 4 v 2828 5169 a(2)2873 5143 y Fr(4)2913 5169 y Fs(\031)2968 5143 y Fr(2)3025 5107 y Fq(j)-15 b(j)p Fs(R)q Fq(j)g(j)3165 5069 y Fr(2)3165 5129 y FA(R)0 5403 y Fz(b)m(y)30 b(\(43\))i(whic)m(h)e(implies)1245 5607 y Fq(j)-15 b(j)p Fs(\032)1327 5621 y Fr(1)p Fo(;)p Fr(0)1422 5607 y Fq(j)g(j)1457 5621 y FA(C)1528 5607 y Fq(\024)1634 5545 y Fs(C)1699 5559 y Fo(R)1756 5545 y Fz(\(log)18 b(\003\))2022 5512 y Fr(1)p Fo(=)p Fr(2)p 1634 5586 500 4 v 1833 5669 a Fz(4)p Fs(\031)2143 5607 y Fq(j)-15 b(j)p Fs(Q)p Fq(j)g(j)2285 5621 y FA(Q)2347 5607 y Fs(:)p 2468 5607 4 62 v 2472 5549 55 4 v 2472 5607 V 2526 5607 4 62 v 1844 5906 a Fz(22)p eop end %%Page: 23 23 TeXDict begin 23 22 bop 0 63 a Fe(4.3.2)105 b(Second)36 b(order)f(terms)0 235 y Fz(T)-8 b(o)31 b(simplify)f(the)g(presen)m (tation,)i(w)m(e)f(in)m(tro)s(duce)f(the)h(follo)m(wing)h(notation:)302 504 y Fs(S)358 518 y Fo(p;q)476 504 y Fz(:=)25 b(\(4)p Fs(\031)s Fz(\)\(2)p Fs(\031)s Fz(\))937 466 y FA(\000)p Fr(3)p Fo(=p)1120 376 y Fp(\022)1187 380 y(Z)1237 586 y Fj(R)1285 567 y Fi(3)1416 442 y Fs(du)p 1349 483 234 4 v 1349 566 a(E)5 b Fz(\()p Fs(u)p Fz(\))1543 540 y Fo(q)1592 376 y Fp(\023)1670 371 y Fi(1)p 1669 383 33 3 v 1669 424 a Fg(p)1730 504 y Fs(;)197 b(S)2008 518 y Fo(p)2073 504 y Fz(:=)25 b Fs(S)2250 518 y Fo(p;p)2345 504 y Fs(;)197 b(K)2644 518 y Fo(p)2709 504 y Fz(:=)2868 442 y(1)p 2840 483 101 4 v 2840 566 a(2)p Fs(\031)2966 380 y Fp(Z)3057 406 y Fr(+)p FA(1)3017 586 y(\0001)3279 442 y Fs(d\021)p 3212 483 232 4 v 3212 566 a(E)5 b Fz(\()p Fs(\021)s Fz(\))3402 540 y Fo(p)3453 504 y Fs(:)0 748 y Fz(Let)31 b(us)f(recall)h(the)g(follo)m(wing)h(inequalit)m(y)f([27)r (,)f(Theorem)g(4.1])959 939 y Fq(j)-15 b(j)p Fs(f)10 b Fz(\()p Fs(x)p Fz(\))p Fs(g)s Fz(\()p Fq(\000)p Fs(i)p Fq(r)p Fz(\))p Fq(j)-14 b(j)1501 966 y Fd(S)1558 974 y Fg(p)1624 939 y Fq(\024)25 b Fz(\(2)p Fs(\031)s Fz(\))1890 902 y FA(\000)p Fr(3)p Fo(=p)2072 939 y Fq(j)-15 b(j)p Fs(f)10 b Fq(j)-16 b(j)2197 966 y Fo(L)2245 947 y Fg(p)2281 966 y Fr(\()p Fj(R)2356 947 y Fi(3)2391 966 y Fr(\))2437 939 y Fq(j)i(j)p Fs(g)s Fq(j)g(j)2555 966 y Fo(L)2603 947 y Fg(p)2639 966 y Fr(\()p Fj(R)2714 947 y Fi(3)2749 966 y Fr(\))2796 939 y Fs(;)797 b Fz(\(44\))0 1131 y(whic)m(h)30 b(implies)1287 1157 y Fp(\014)1287 1211 y(\014)1287 1266 y(\014)1287 1320 y(\014)1302 1157 y(\014)1302 1211 y(\014)1302 1266 y(\014)1302 1320 y(\014)1423 1227 y Fz(1)p 1343 1267 207 4 v 1343 1351 a Fq(j)p Fs(D)1443 1365 y Fr(0)1483 1351 y Fq(j)1508 1324 y Fo(a)1560 1288 y Fs(f)1615 1157 y Fp(\014)1615 1211 y(\014)1615 1266 y(\014)1615 1320 y(\014)1629 1157 y(\014)1629 1211 y(\014)1629 1266 y(\014)1629 1320 y(\014)1659 1379 y Fd(S)1716 1387 y Fg(p)1782 1288 y Fq(\024)1888 1226 y Fs(S)1944 1240 y Fo(p;ap)p 1888 1267 189 4 v 1932 1351 a Fz(4)p Fs(\031)2101 1288 y Fq(j)-15 b(j)p Fs(f)10 b Fq(j)-15 b(j)2226 1315 y Fo(L)2274 1296 y Fg(p)2310 1315 y Fr(\()p Fj(R)2385 1296 y Fi(3)2420 1315 y Fr(\))2467 1288 y Fs(:)141 1516 y Fz(On)30 b(the)g(other)h (hand,)e(w)m(e)i(shall)g(often)g(use)f(the)g(follo)m(wing)i(tric)m(k) 514 1707 y(\()p Fs(E)5 b Fz(\()p Fs(p)p Fz(\))737 1670 y Fr(2)798 1707 y Fz(+)20 b Fs(\021)937 1670 y Fr(2)977 1707 y Fz(\)\()p Fs(E)5 b Fz(\()p Fs(q)s Fz(\))1233 1670 y Fr(2)1294 1707 y Fz(+)20 b Fs(\021)1433 1670 y Fr(2)1473 1707 y Fz(\))83 b(=)g(\()p Fs(E)5 b Fz(\()p Fs(p)p Fz(\))p Fs(E)g Fz(\()p Fs(q)s Fz(\)\))2189 1670 y Fr(2)2251 1707 y Fz(+)20 b(\()p Fs(E)5 b Fz(\()p Fs(p)p Fz(\))2565 1670 y Fr(2)2626 1707 y Fz(+)20 b Fs(E)5 b Fz(\()p Fs(q)s Fz(\))2903 1670 y Fr(2)2943 1707 y Fz(\))p Fs(\021)3026 1670 y Fr(2)3086 1707 y Fz(+)20 b Fs(\021)3225 1670 y Fr(4)1591 1883 y Fq(\025)1755 1822 y Fz(1)p 1755 1862 46 4 v 1755 1945 a(4)1810 1883 y Fs(E)5 b Fz(\()p Fs(p)21 b Fz(+)f Fs(q)s Fz(\))2154 1846 y Fr(2)2214 1883 y Fz(+)2315 1822 y(1)p 2315 1862 V 2315 1945 a(2)2370 1883 y Fs(E)5 b Fz(\()p Fs(p)21 b Fz(+)f Fs(q)s Fz(\))2714 1846 y Fr(2)2753 1883 y Fs(\021)2801 1846 y Fr(2)1591 2099 y Fq(\025)1755 2037 y Fz(1)p 1755 2078 V 1755 2161 a(4)1810 2099 y Fs(E)5 b Fz(\()p Fs(p)21 b Fz(+)f Fs(q)s Fz(\))2154 2061 y Fr(2)2194 2099 y Fs(E)5 b Fz(\()p Fs(\021)s Fz(\))2384 2061 y Fr(2)0 2311 y Fz(b)m(y)30 b(Lemma)h(5.)41 b(This)29 b(implies)1516 2474 y(1)p 1022 2514 1035 4 v 1022 2533 a Fp(p)p 1113 2533 428 4 v 78 x Fs(E)5 b Fz(\()p Fs(p)p Fz(\))1301 2584 y Fr(2)1361 2611 y Fz(+)20 b Fs(\021)1500 2584 y Fr(2)1540 2533 y Fp(p)p 1631 2533 426 4 v 78 x Fs(E)5 b Fz(\()p Fs(q)s Fz(\))1817 2584 y Fr(2)1877 2611 y Fz(+)20 b Fs(\021)2016 2584 y Fr(2)2091 2535 y Fq(\024)2442 2474 y Fz(2)p 2197 2514 536 4 v 2197 2598 a Fs(E)5 b Fz(\()p Fs(p)21 b Fz(+)f Fs(q)s Fz(\))p Fs(E)5 b Fz(\()p Fs(\021)s Fz(\))2742 2535 y Fs(:)851 b Fz(\(45\))141 2930 y(Recall)32 b(no)m(w)f(that)f(w)m(e)h(ha)m(v)m(e)h Fs(Q)1217 2944 y Fr(2)1281 2930 y Fz(=)25 b Fs(Q)1449 2944 y Fr(2)p Fo(;)p Fr(0)1564 2930 y Fz(+)20 b Fs(Q)1727 2944 y Fr(1)p Fo(;)p Fr(1)1841 2930 y Fz(+)g Fs(Q)2004 2944 y Fr(0)p Fo(;)p Fr(2)2129 2930 y Fz(with)29 3181 y Fs(Q)101 3195 y Fr(2)p Fo(;)p Fr(0)279 3181 y Fz(=)82 b Fq(\000)540 3120 y Fz(1)p 513 3160 101 4 v 513 3244 a(2)p Fs(\031)639 3057 y Fp(Z)729 3084 y Fr(+)p FA(1)689 3264 y(\0001)874 3181 y Fs(d\021)1111 3120 y Fz(1)p 979 3160 309 4 v 979 3244 a Fs(D)1057 3217 y Fr(0)1117 3244 y Fz(+)20 b Fs(i\021)1298 3181 y(R)1509 3120 y Fz(1)p 1378 3160 V 1378 3244 a Fs(D)1456 3217 y Fr(0)1515 3244 y Fz(+)g Fs(i\021)1696 3181 y(R)1907 3120 y Fz(1)p 1776 3160 V 1776 3244 a Fs(D)1854 3217 y Fr(0)1913 3244 y Fz(+)g Fs(i\021)29 3441 y(Q)101 3455 y Fr(1)p Fo(;)p Fr(1)279 3441 y Fz(=)470 3380 y(1)p 442 3420 101 4 v 442 3504 a(2)p Fs(\031)568 3318 y Fp(Z)659 3344 y Fr(+)p FA(1)618 3524 y(\0001)804 3441 y Fs(d\021)1041 3380 y Fz(1)p 909 3420 309 4 v 909 3504 a Fs(D)987 3477 y Fr(0)1047 3504 y Fz(+)g Fs(i\021)1227 3441 y(R)1438 3380 y Fz(1)p 1307 3420 V 1307 3504 a Fs(D)1385 3477 y Fr(0)1444 3504 y Fz(+)g Fs(i\021)1625 3441 y(')1684 3404 y FA(0)1849 3380 y Fz(1)p 1718 3420 V 1718 3504 a Fs(D)1796 3477 y Fr(0)1855 3504 y Fz(+)g Fs(i\021)2056 3441 y Fz(+)2184 3380 y(1)p 2157 3420 101 4 v 2157 3504 a(2)p Fs(\031)2282 3318 y Fp(Z)2373 3344 y Fr(+)p FA(1)2333 3524 y(\0001)2518 3441 y Fs(d\021)2755 3380 y Fz(1)p 2623 3420 309 4 v 2623 3504 a Fs(D)2701 3477 y Fr(0)2761 3504 y Fz(+)g Fs(i\021)2942 3441 y(')3001 3404 y FA(0)3166 3380 y Fz(1)p 3034 3420 V 3034 3504 a Fs(D)3112 3477 y Fr(0)3172 3504 y Fz(+)g Fs(i\021)3353 3441 y(R)3564 3380 y Fz(1)p 3433 3420 V 3433 3504 a Fs(D)3511 3477 y Fr(0)3570 3504 y Fz(+)g Fs(i\021)29 3702 y(Q)101 3716 y Fr(0)p Fo(;)p Fr(2)279 3702 y Fz(=)82 b Fq(\000)540 3640 y Fz(1)p 513 3681 101 4 v 513 3764 a(2)p Fs(\031)639 3578 y Fp(Z)729 3604 y Fr(+)p FA(1)689 3784 y(\0001)874 3702 y Fs(d\021)1111 3640 y Fz(1)p 979 3681 309 4 v 979 3764 a Fs(D)1057 3738 y Fr(0)1117 3764 y Fz(+)20 b Fs(i\021)1298 3702 y(')1357 3664 y FA(0)1522 3640 y Fz(1)p 1391 3681 V 1391 3764 a Fs(D)1469 3738 y Fr(0)1528 3764 y Fz(+)g Fs(i\021)1709 3702 y(')1768 3664 y FA(0)1933 3640 y Fz(1)p 1801 3681 V 1801 3764 a Fs(D)1879 3738 y Fr(0)1939 3764 y Fz(+)g Fs(i\021)2119 3702 y(:)0 3941 y Fz(W)-8 b(e)32 b(shall)e(no)m(w)h(treat)g(eac)m(h)h(term)e(separately)-8 b(.)0 4117 y Fe(Lemma)35 b(11.)42 b Fy(We)32 b(have)h Fs(\032)967 4131 y Fr(0)p Fo(;)p Fr(2)1087 4117 y Fz(=)25 b(0)33 b Fy(and)g(the)g(fol)5 b(lowing)34 b(estimates:)481 4318 y Fq(j)-15 b(j)p Fs(Q)588 4332 y Fr(2)p Fo(;)p Fr(0)683 4318 y Fq(j)g(j)718 4332 y FA(Q)805 4318 y Fq(\024)25 b Fz(2)946 4280 y Fr(5)p Fo(=)p Fr(2)1057 4318 y Fs(K)1134 4337 y Fr(3)p Fo(=)p Fr(2)1244 4318 y Fz(\()p Fs(C)1344 4332 y Fo(R)1402 4318 y Fz(\))1437 4280 y Fr(2)1477 4318 y Fq(j)-15 b(j)p Fs(Q)p Fq(j)g(j)1619 4280 y Fr(2)1619 4340 y FA(Q)1681 4318 y Fs(;)202 b Fq(j)-15 b(j)p Fs(Q)2015 4332 y Fr(1)p Fo(;)p Fr(1)2109 4318 y Fq(j)g(j)2144 4332 y FA(Q)2231 4318 y Fq(\024)25 b Fz(4)p Fs(S)2428 4332 y Fr(6)2468 4318 y Fs(C)2533 4332 y Fr(6)2572 4318 y Fs(K)2649 4337 y Fr(3)p Fo(=)p Fr(2)2760 4318 y Fs(C)2825 4332 y Fo(R)2882 4318 y Fq(j)-15 b(j)p Fs(Q)p Fq(j)g(j)3024 4332 y FA(Q)3087 4318 y Fq(j)g(j)p Fs(\032)3169 4280 y FA(0)3192 4318 y Fq(j)g(j)3227 4332 y FA(C)3273 4318 y Fs(;)1269 4527 y Fq(j)g(j)p Fs(Q)1376 4541 y Fr(0)p Fo(;)p Fr(2)1470 4527 y Fq(j)g(j)1505 4541 y FA(Q)1593 4527 y Fq(\024)25 b Fz(2)1734 4447 y Fq(p)p 1810 4447 91 4 v 80 x Fz(10)q Fs(S)1957 4541 y Fr(6)p Fo(;)p Fr(5)2051 4527 y Fs(C)2116 4541 y Fo(M)2195 4527 y Fs(C)2260 4541 y Fr(6)2299 4527 y Fq(j)-15 b(j)p Fs(\032)2381 4489 y FA(0)2405 4527 y Fq(j)g(j)2440 4489 y Fr(2)2440 4549 y FA(C)2485 4527 y Fs(;)569 4746 y Fq(j)g(j)p Fs(\032)651 4760 y Fr(2)p Fo(;)p Fr(0)746 4746 y Fq(j)g(j)781 4760 y FA(C)851 4746 y Fq(\024)957 4685 y Fs(S)1013 4699 y Fr(6)1052 4685 y Fs(C)1117 4699 y Fr(6)1157 4685 y Fz(\()p Fs(C)1257 4699 y Fo(R)1315 4685 y Fz(\))1350 4652 y Fr(2)p 957 4725 433 4 v 1146 4809 a Fs(\031)1400 4746 y Fq(j)g(j)p Fs(Q)p Fq(j)g(j)1542 4709 y Fr(2)1542 4769 y FA(Q)1604 4746 y Fs(;)201 b Fq(j)-15 b(j)p Fs(\032)1912 4760 y Fr(1)p Fo(;)p Fr(1)2007 4746 y Fq(j)g(j)2042 4760 y FA(C)2113 4746 y Fq(\024)24 b Fz(4)2263 4684 y Fs(S)2319 4698 y Fr(6)p Fo(;)p Fr(5)2414 4684 y Fs(C)2479 4698 y Fo(M)2558 4684 y Fs(C)2623 4698 y Fr(6)2662 4684 y Fs(C)2727 4698 y Fo(R)p 2263 4725 522 4 v 2497 4809 a Fs(\031)2795 4746 y Fq(j)-15 b(j)p Fs(\032)2877 4709 y FA(0)2901 4746 y Fq(j)g(j)2936 4760 y FA(C)2981 4746 y Fq(j)g(j)p Fs(Q)p Fq(j)g(j)3123 4760 y FA(Q)3185 4746 y Fs(;)0 4928 y Fy(and)34 b(so)1374 5040 y Fq(j)-15 b(j)p Fz(\()p Fs(Q)1516 5054 y Fr(2)1556 5040 y Fs(;)15 b(\032)1643 5054 y Fr(2)1683 5040 y Fz(\))p Fq(j)-15 b(j)26 b(\024)f Fs(\024)1927 5054 y Fr(2)1982 4963 y Fp(\014)1982 5018 y(\014)1997 4963 y(\014)1997 5018 y(\014)2027 5040 y Fz(\()p Fs(Q;)15 b(\032)2221 5003 y FA(0)2245 5040 y Fz(\))2280 4963 y Fp(\014)2280 5018 y(\014)2296 4963 y(\014)2296 5018 y(\014)2326 4990 y Fr(2)2380 5040 y Fs(;)0 5201 y Fy(with)1355 5314 y Fs(\024)1407 5328 y Fr(2)1472 5314 y Fz(=)25 b Fs(C)1633 5328 y Fo(Q)1689 5337 y Fi(2)1728 5314 y Fs(C)1793 5328 y Fo(R)1850 5234 y Fq(p)p 1926 5234 46 4 v 80 x Fz(2)c(+)f(2)2128 5244 y Fq(p)p 2204 5244 56 4 v 70 x Fs(\031)s(C)2324 5328 y Fo(\032)2360 5337 y Fi(2)2399 5314 y Fs(;)85 5556 y(C)150 5570 y Fo(Q)206 5579 y Fi(2)270 5556 y Fz(=)25 b(max)550 5400 y Fp( )622 5556 y Fz(2)667 5518 y Fr(3)p Fo(=)p Fr(2)778 5556 y Fs(K)855 5574 y Fr(3)p Fo(=)p Fr(2)980 5556 y Fs(;)1045 5485 y(S)1101 5499 y Fr(6)1141 5485 y Fs(C)1206 5499 y Fr(6)1245 5485 y Fs(K)1322 5504 y Fr(3)p Fo(=)p Fr(2)p 1045 5535 387 4 v 1151 5553 a Fq(p)p 1226 5553 101 4 v 1226 5628 a Fz(2)p Fs(\031)1457 5556 y(;)1523 5418 y Fq(p)p 1599 5418 46 4 v 76 x Fz(5)p Fs(S)1700 5508 y Fr(6)p Fo(;)p Fr(5)1794 5494 y Fs(C)1859 5508 y Fo(M)1938 5494 y Fs(C)2003 5508 y Fr(6)p 1523 5535 520 4 v 1695 5628 a Fs(\031)1750 5553 y Fq(p)p 1825 5553 46 4 v 1825 5628 a Fz(2)2053 5400 y Fp(!)2140 5556 y Fs(;)201 b(C)2431 5570 y Fo(\032)2467 5579 y Fi(2)2531 5556 y Fz(=)25 b(max)2811 5427 y Fp(\022)2888 5494 y Fs(S)2944 5508 y Fr(6)2983 5494 y Fs(C)3048 5508 y Fr(6)p 2888 5535 200 4 v 2938 5618 a Fz(2)p Fs(\031)3113 5556 y(;)3178 5494 y(S)3234 5508 y Fr(6)p Fo(;)p Fr(5)3328 5494 y Fs(C)3393 5508 y Fo(M)3472 5494 y Fs(C)3537 5508 y Fr(6)p 3178 5535 399 4 v 3234 5628 a Fs(\031)3289 5602 y Fr(3)p Fo(=)p Fr(2)3400 5553 y Fq(p)p 3475 5553 46 4 v 3475 5628 a Fz(2)3587 5427 y Fp(\023)3669 5556 y Fs(:)1844 5906 y Fz(23)p eop end %%Page: 24 24 TeXDict begin 24 23 bop 0 63 a Fy(Pr)-5 b(o)g(of)34 b({)63 b Fe(Step)35 b(1)g(:)47 b(Estimates)34 b(on)h(the)f(exc)m(hange)i(term) f Fs(Q)2339 77 y Fr(2)2378 63 y Fe(.)0 176 y Fq(\017)61 b Fs(Q)178 190 y Fr(2)p Fo(;)p Fr(0)272 176 y Fz(.)41 b(T)-8 b(o)31 b(estimate)h Fs(Q)908 190 y Fr(2)p Fo(;)p Fr(0)1002 176 y Fz(,)f(w)m(e)f(write)404 418 y Fq(j)446 395 y Fp(d)429 418 y Fs(Q)501 432 y Fr(2)p Fo(;)p Fr(0)595 418 y Fz(\()p Fs(p;)15 b(q)s Fz(\))p Fq(j)26 b(\024)980 356 y Fz(1)p 952 397 101 4 v 952 480 a(2)p Fs(\031)1078 294 y Fp(Z)1169 320 y Fr(+)p FA(1)1128 500 y(\0001)1313 418 y Fs(d\021)1424 294 y Fp(Z)1475 500 y Fj(R)1523 481 y Fi(3)1592 418 y Fs(dp)1685 432 y Fr(1)1812 356 y Fq(j)1855 333 y Fp(b)1837 356 y Fs(R)q Fz(\()p Fs(p;)15 b(p)2074 370 y Fr(1)2114 356 y Fz(\))p Fq(j)p 1734 397 519 4 v 1734 415 a Fp(p)p 1825 415 428 4 v 78 x Fs(E)5 b Fz(\()p Fs(p)p Fz(\))2013 467 y Fr(2)2074 493 y Fz(+)20 b Fs(\021)2213 467 y Fr(2)2371 356 y Fq(j)2413 333 y Fp(b)2396 356 y Fs(R)q Fz(\()p Fs(p)2547 370 y Fr(1)2586 356 y Fs(;)15 b(q)s Fz(\))p Fq(j)p 2272 397 558 4 v 2272 415 a Fp(p)p 2363 415 467 4 v 78 x Fs(E)5 b Fz(\()p Fs(p)2516 507 y Fr(1)2556 493 y Fz(\))2591 467 y Fr(2)2651 493 y Fz(+)20 b Fs(\021)2790 467 y Fr(2)3085 356 y Fz(1)p 2850 397 517 4 v 2850 415 a Fp(p)p 2941 415 426 4 v 78 x Fs(E)5 b Fz(\()p Fs(q)s Fz(\))3127 467 y Fr(2)3187 493 y Fz(+)20 b Fs(\021)3326 467 y Fr(2)0 654 y Fz(and)30 b(so)g(b)m(y)h(\(45\))348 892 y Fq(j)391 869 y Fp(d)373 892 y Fs(Q)445 906 y Fr(2)p Fo(;)p Fr(0)540 892 y Fz(\()p Fs(p;)15 b(q)s Fz(\))p Fq(j)26 b(\024)897 830 y Fz(2)942 797 y Fr(3)p Fo(=)p Fr(2)p 897 871 156 4 v 924 954 a Fz(2)p Fs(\031)1077 768 y Fp(Z)1168 794 y Fr(+)p FA(1)1128 974 y(\0001)1653 830 y Fs(d\021)p 1323 871 756 4 v 1323 958 a(E)5 b Fz(\()p Fs(\021)s Fz(\))1513 931 y Fr(3)p Fo(=)p Fr(2)1624 958 y Fs(E)g Fz(\()p Fs(p)21 b Fz(+)f Fs(q)s Fz(\))1968 931 y Fr(1)p Fo(=)p Fr(2)2103 768 y Fp(Z)2154 974 y Fj(R)2202 955 y Fi(3)2332 830 y Fq(j)2374 807 y Fp(b)2357 830 y Fs(R)q Fz(\()p Fs(p;)15 b(p)2594 844 y Fr(1)2634 830 y Fz(\))p Fq(j)p 2266 871 496 4 v 2266 958 a Fs(E)5 b Fz(\()p Fs(p)20 b Fz(+)g Fs(p)2576 972 y Fr(1)2615 958 y Fz(\))2650 931 y Fr(1)p Fo(=)p Fr(2)2847 830 y Fq(j)2889 807 y Fp(b)2872 830 y Fs(R)q Fz(\()p Fs(p)3023 844 y Fr(1)3063 830 y Fs(;)15 b(q)s Fz(\))p Fq(j)p 2781 871 494 4 v 2781 958 a Fs(E)5 b Fz(\()p Fs(p)2934 972 y Fr(1)2994 958 y Fz(+)20 b Fs(q)s Fz(\))3164 931 y Fr(1)p Fo(=)p Fr(2)3299 892 y Fs(dp)3392 906 y Fr(1)0 1109 y Fz(whic)m(h)30 b(implies)127 1342 y Fs(E)5 b Fz(\()p Fs(p)21 b Fq(\000)f Fs(q)s Fz(\))p Fs(E)5 b Fz(\()p Fs(p)21 b Fz(+)f Fs(q)s Fz(\))815 1304 y Fr(1)p Fo(=)p Fr(2)925 1342 y Fq(j)968 1319 y Fp(d)950 1342 y Fs(Q)1022 1356 y Fr(2)p Fo(;)p Fr(0)1116 1342 y Fz(\()p Fs(p;)15 b(q)s Fz(\))p Fq(j)27 b(\024)e Fz(2)1509 1304 y Fr(5)p Fo(=)p Fr(2)1619 1342 y Fs(K)1696 1360 y Fr(3)p Fo(=)p Fr(2)1821 1218 y Fp(Z)1872 1424 y Fj(R)1920 1406 y Fi(3)1984 1280 y Fs(E)5 b Fz(\()p Fs(p)20 b Fq(\000)g Fs(p)2294 1294 y Fr(1)2333 1280 y Fz(\))p Fq(j)2411 1258 y Fp(b)2393 1280 y Fs(R)r Fz(\()p Fs(p;)15 b(p)2631 1294 y Fr(1)2670 1280 y Fz(\))p Fq(j)p 1984 1321 748 4 v 2110 1408 a Fs(E)5 b Fz(\()p Fs(p)20 b Fz(+)g Fs(p)2420 1422 y Fr(1)2460 1408 y Fz(\))2495 1382 y Fr(1)p Fo(=)p Fr(2)2751 1280 y Fs(E)5 b Fz(\()p Fs(p)2904 1294 y Fr(1)2964 1280 y Fq(\000)20 b Fs(q)s Fz(\))p Fq(j)3177 1258 y Fp(b)3159 1280 y Fs(R)q Fz(\()p Fs(p)3310 1294 y Fr(1)3350 1280 y Fs(;)15 b(q)s Fz(\))p Fq(j)p 2751 1321 744 4 v 2876 1408 a Fs(E)5 b Fz(\()p Fs(p)3029 1422 y Fr(1)3089 1408 y Fz(+)20 b Fs(q)s Fz(\))3259 1382 y Fr(1)p Fo(=)p Fr(2)3520 1342 y Fs(dp)3613 1356 y Fr(1)0 1559 y Fz(and)30 b(\014nally)943 1672 y Fq(j)-15 b(j)p Fs(Q)1050 1686 y Fr(2)p Fo(;)p Fr(0)1144 1672 y Fq(j)g(j)1179 1686 y FA(Q)1267 1672 y Fq(\024)25 b Fz(2)1408 1634 y Fr(5)p Fo(=)p Fr(2)1518 1672 y Fs(K)1595 1691 y Fr(3)p Fo(=)p Fr(2)1705 1672 y Fq(j)-15 b(j)p Fs(R)q Fq(j)g(j)1845 1634 y Fr(2)1845 1694 y FA(R)1936 1672 y Fq(\024)25 b Fz(2)2077 1634 y Fr(5)p Fo(=)p Fr(2)2187 1672 y Fs(K)2264 1691 y Fr(3)p Fo(=)p Fr(2)2374 1672 y Fz(\()p Fs(C)2474 1686 y Fo(R)2532 1672 y Fz(\))2567 1634 y Fr(2)2607 1672 y Fq(j)-15 b(j)p Fs(Q)p Fq(j)g(j)2749 1634 y Fr(2)2749 1694 y FA(Q)2811 1672 y Fs(:)0 1898 y Fq(\017)61 b Fs(Q)178 1912 y Fr(1)p Fo(;)p Fr(1)272 1898 y Fz(.)41 b(W)-8 b(e)31 b(treat)h(for)e(instance)841 2127 y Fs(Q)913 2090 y FA(0)913 2150 y Fr(1)p Fo(;)p Fr(1)1033 2127 y Fz(:=)1282 2066 y(1)p 1164 2106 282 4 v 1164 2194 a(\(2)p Fs(\031)s Fz(\))1334 2167 y Fr(5)p Fo(=)p Fr(2)1470 2004 y Fp(Z)1561 2030 y Fr(+)p FA(1)1521 2210 y(\0001)1706 2127 y Fs(d\021)1943 2066 y Fz(1)p 1811 2106 309 4 v 1811 2190 a Fs(D)1889 2163 y Fr(0)1949 2190 y Fz(+)20 b Fs(i\021)2130 2127 y(R)2341 2066 y Fz(1)p 2210 2106 V 2210 2190 a Fs(D)2288 2163 y Fr(0)2347 2190 y Fz(+)g Fs(i\021)2527 2127 y(')2586 2090 y FA(0)2751 2066 y Fz(1)p 2620 2106 V 2620 2190 a Fs(D)2698 2163 y Fr(0)2758 2190 y Fz(+)f Fs(i\021)0 2345 y Fz(and)30 b(use)g(the)g(same)h(metho)s(d)f(to)h(obtain)83 2572 y Fs(E)5 b Fz(\()p Fs(p)21 b Fq(\000)f Fs(q)s Fz(\))p Fs(E)5 b Fz(\()p Fs(p)20 b Fz(+)g Fs(q)s Fz(\))770 2535 y Fr(1)p Fo(=)p Fr(2)881 2572 y Fq(j)923 2543 y Fp(d)906 2572 y Fs(Q)978 2541 y FA(0)978 2598 y Fr(1)p Fo(;)p Fr(1)1072 2572 y Fz(\()p Fs(p;)15 b(q)s Fz(\))p Fq(j)26 b(\024)1547 2511 y Fz(4)p 1429 2551 282 4 v 1429 2639 a(\(2)p Fs(\031)s Fz(\))1599 2612 y Fr(5)p Fo(=)p Fr(2)1735 2449 y Fp(Z)1826 2475 y Fr(+)p FA(1)1786 2655 y(\0001)2029 2511 y Fs(d\021)p 1981 2551 192 4 v 1981 2635 a(E)5 b Fz(\()p Fs(\021)s Fz(\))2183 2572 y Fq(\002)686 2825 y(\002)777 2701 y Fp(Z)827 2907 y Fj(R)875 2888 y Fi(3)994 2763 y Fs(E)g Fz(\()p Fs(p)21 b Fq(\000)f Fs(p)1305 2777 y Fr(1)1344 2763 y Fz(\))p 939 2804 496 4 v 939 2891 a Fs(E)5 b Fz(\()p Fs(p)21 b Fz(+)f Fs(p)1250 2905 y Fr(1)1289 2891 y Fz(\))1324 2864 y Fr(1)p Fo(=)p Fr(2)1444 2825 y Fq(j)1486 2802 y Fp(b)1469 2825 y Fs(R)q Fz(\()p Fs(p;)15 b(p)1706 2839 y Fr(1)1746 2825 y Fz(\))p Fq(j)2251 2763 y Fs(E)5 b Fz(\()p Fs(p)2404 2777 y Fr(1)2464 2763 y Fq(\000)20 b Fs(q)s Fz(\))p 1816 2804 1254 4 v 1816 2891 a(\()p Fs(E)5 b Fz(\()p Fs(p)2004 2905 y Fr(1)2044 2891 y Fz(\))2079 2865 y Fr(2)2139 2891 y Fz(+)20 b Fs(\021)2278 2865 y Fr(2)2318 2891 y Fz(\))2353 2864 y Fr(1)p Fo(=)p Fr(4)2464 2891 y Fz(\()p Fs(E)5 b Fz(\()p Fs(q)s Fz(\))2685 2865 y Fr(2)2745 2891 y Fz(+)20 b Fs(\021)2884 2865 y Fr(2)2924 2891 y Fz(\))2959 2864 y Fr(1)p Fo(=)p Fr(4)3080 2825 y Fq(j)3121 2801 y Fp(b)3105 2825 y Fs(')3164 2798 y FA(0)3188 2825 y Fz(\()p Fs(p)3269 2839 y Fr(1)3328 2825 y Fq(\000)g Fs(q)s Fz(\))p Fq(j)15 b Fs(dp)3631 2839 y Fr(1)3671 2825 y Fs(:)0 3042 y Fz(This)30 b(means)g(that)610 3244 y Fq(j)-15 b(j)p Fs(Q)717 3207 y FA(0)717 3267 y Fr(1)p Fo(;)p Fr(1)811 3244 y Fq(j)g(j)846 3258 y FA(Q)934 3244 y Fq(\024)1067 3183 y Fz(4)p 1039 3223 101 4 v 1039 3307 a(2)p Fs(\031)1165 3121 y Fp(Z)1256 3147 y Fr(+)p FA(1)1216 3327 y(\0001)1459 3183 y Fs(d\021)p 1411 3223 192 4 v 1411 3307 a(E)5 b Fz(\()p Fs(\021)s Fz(\))1627 3112 y Fp(\014)1627 3167 y(\014)1627 3222 y(\014)1627 3276 y(\014)1642 3112 y(\014)1642 3167 y(\014)1642 3222 y(\014)1642 3276 y(\014)1673 3244 y Fs(R)1743 3207 y FA(0)2045 3183 y Fz(1)p 1776 3223 585 4 v 1776 3311 a(\()p Fq(j)p Fs(D)1911 3325 y Fr(0)1951 3311 y Fq(j)1976 3284 y Fr(2)2036 3311 y Fz(+)20 b Fs(\021)2175 3284 y Fr(2)2215 3311 y Fz(\))2250 3284 y Fr(1)p Fo(=)p Fr(4)2370 3244 y Fs(f)2704 3183 y Fz(1)p 2434 3223 V 2434 3311 a(\()p Fq(j)p Fs(D)2569 3325 y Fr(0)2610 3311 y Fq(j)2635 3284 y Fr(2)2694 3311 y Fz(+)g Fs(\021)2833 3284 y Fr(2)2873 3311 y Fz(\))2908 3284 y Fr(1)p Fo(=)p Fr(4)3029 3112 y Fp(\014)3029 3167 y(\014)3029 3222 y(\014)3029 3276 y(\014)3044 3112 y(\014)3044 3167 y(\014)3044 3222 y(\014)3044 3276 y(\014)3074 3337 y Fd(S)3131 3346 y Fi(2)0 3482 y Fz(where)30 b(w)m(e)h(ha)m(v)m(e)g(in)m(tro)s(duced)f Fs(R)1131 3449 y FA(0)1184 3482 y Fz(and)g Fs(f)40 b Fz(de\014ned)29 b(b)m(y)811 3670 y Fp(c)810 3694 y Fs(R)880 3668 y FA(0)903 3694 y Fz(\()p Fs(p;)15 b(q)s Fz(\))26 b(:=)1315 3632 y Fs(E)5 b Fz(\()p Fs(p)20 b Fq(\000)g Fs(q)s Fz(\))p 1260 3673 454 4 v 1260 3760 a Fs(E)5 b Fz(\()p Fs(p)20 b Fz(+)g Fs(q)s Fz(\))1603 3734 y Fr(1)p Fo(=)p Fr(2)1723 3694 y Fq(j)1766 3671 y Fp(b)1748 3694 y Fs(R)q Fz(\()p Fs(p;)15 b(q)s Fz(\))p Fq(j)p Fs(;)2193 3670 y Fp(b)2176 3694 y Fs(f)9 b Fz(\()p Fs(k)s Fz(\))26 b(:=)f Fs(E)5 b Fz(\()p Fs(k)s Fz(\))p Fq(j)2732 3670 y Fp(b)2714 3694 y Fs(')2773 3668 y FA(0)2799 3694 y Fz(\()p Fs(k)s Fz(\))p Fq(j)p Fs(:)0 3910 y Fz(But)31 b(no)m(w)216 3975 y Fp(\014)216 4030 y(\014)216 4084 y(\014)216 4139 y(\014)216 4193 y(\014)231 3975 y(\014)231 4030 y(\014)231 4084 y(\014)231 4139 y(\014)231 4193 y(\014)261 4134 y Fs(R)331 4097 y FA(0)606 4073 y Fz(1)p 364 4113 529 4 v 364 4219 a(\()p Fq(j)p Fs(D)499 4233 y Fr(0)540 4219 y Fq(j)565 4193 y Fr(2)625 4219 y Fz(+)20 b Fs(\021)764 4193 y Fr(2)803 4219 y Fz(\))848 4156 y Fi(1)p 849 4168 31 3 v 849 4209 a(4)903 4134 y Fs(f)1209 4073 y Fz(1)p 968 4113 529 4 v 968 4219 a(\()p Fq(j)p Fs(D)1103 4233 y Fr(0)1143 4219 y Fq(j)1168 4193 y Fr(2)1228 4219 y Fz(+)g Fs(\021)1367 4193 y Fr(2)1406 4219 y Fz(\))1451 4156 y Fi(1)p 1452 4168 31 3 v 1452 4209 a(4)1506 3975 y Fp(\014)1506 4030 y(\014)1506 4084 y(\014)1506 4139 y(\014)1506 4193 y(\014)1521 3975 y(\014)1521 4030 y(\014)1521 4084 y(\014)1521 4139 y(\014)1521 4193 y(\014)1552 4252 y Fd(S)1609 4261 y Fi(2)1731 4134 y Fq(\024)1884 4057 y Fp(\014)1884 4111 y(\014)1900 4057 y(\014)1900 4111 y(\014)1930 4134 y Fs(R)2000 4097 y FA(0)2023 4057 y Fp(\014)2023 4111 y(\014)2038 4057 y(\014)2038 4111 y(\014)2068 4170 y Fd(S)2125 4179 y Fi(2)2179 3975 y Fp(\014)2179 4030 y(\014)2179 4084 y(\014)2179 4139 y(\014)2179 4193 y(\014)2194 3975 y(\014)2194 4030 y(\014)2194 4084 y(\014)2194 4139 y(\014)2194 4193 y(\014)2476 4073 y Fz(1)p 2235 4113 529 4 v 2235 4219 a(\()p Fq(j)p Fs(D)2370 4233 y Fr(0)2410 4219 y Fq(j)2435 4193 y Fr(2)2495 4219 y Fz(+)g Fs(\021)2634 4193 y Fr(2)2674 4219 y Fz(\))2719 4156 y Fi(1)p 2719 4168 31 3 v 2719 4209 a(4)2774 4134 y Fs(f)3079 4073 y Fz(1)p 2838 4113 529 4 v 2838 4219 a(\()p Fq(j)p Fs(D)2973 4233 y Fr(0)3013 4219 y Fq(j)3038 4193 y Fr(2)3098 4219 y Fz(+)g Fs(\021)3237 4193 y Fr(2)3277 4219 y Fz(\))3322 4156 y Fi(1)p 3322 4168 31 3 v 3322 4209 a(4)3377 3975 y Fp(\014)3377 4030 y(\014)3377 4084 y(\014)3377 4139 y(\014)3377 4193 y(\014)3392 3975 y(\014)3392 4030 y(\014)3392 4084 y(\014)3392 4139 y(\014)3392 4193 y(\014)3422 4252 y Fd(S)3479 4260 y Fl(1)1731 4453 y Fq(\024)82 b(j)-15 b(j)p Fs(R)q Fq(j)g(j)2024 4467 y FA(R)2104 4294 y Fp(\014)2104 4349 y(\014)2104 4403 y(\014)2104 4458 y(\014)2104 4513 y(\014)2119 4294 y(\014)2119 4349 y(\014)2119 4403 y(\014)2119 4458 y(\014)2119 4513 y(\014)2401 4392 y Fz(1)p 2160 4433 529 4 v 2160 4539 a(\()p Fq(j)p Fs(D)2295 4553 y Fr(0)2335 4539 y Fq(j)2360 4512 y Fr(2)2420 4539 y Fz(+)20 b Fs(\021)2559 4512 y Fr(2)2599 4539 y Fz(\))2644 4476 y Fi(1)p 2644 4488 31 3 v 2644 4529 a(4)2699 4453 y Fs(f)3004 4392 y Fz(1)p 2763 4433 529 4 v 2763 4539 a(\()p Fq(j)p Fs(D)2898 4553 y Fr(0)2938 4539 y Fq(j)2963 4512 y Fr(2)3023 4539 y Fz(+)g Fs(\021)3162 4512 y Fr(2)3202 4539 y Fz(\))3247 4476 y Fi(1)p 3247 4488 31 3 v 3247 4529 a(4)3302 4294 y Fp(\014)3302 4349 y(\014)3302 4403 y(\014)3302 4458 y(\014)3302 4513 y(\014)3317 4294 y(\014)3317 4349 y(\014)3317 4403 y(\014)3317 4458 y(\014)3317 4513 y(\014)3347 4571 y Fd(S)3404 4580 y Fi(6)3458 4453 y Fs(:)0 4714 y Fz(If)30 b(w)m(e)h(no)m(w)f(use)g(inequalit)m(y)i(\(44\),)g(w)m(e)f(obtain)311 4908 y Fp(\014)311 4963 y(\014)311 5017 y(\014)311 5072 y(\014)311 5126 y(\014)326 4908 y(\014)326 4963 y(\014)326 5017 y(\014)326 5072 y(\014)326 5126 y(\014)608 5006 y Fz(1)p 367 5046 529 4 v 367 5152 a(\()p Fq(j)p Fs(D)502 5166 y Fr(0)542 5152 y Fq(j)567 5126 y Fr(2)627 5152 y Fz(+)20 b Fs(\021)766 5126 y Fr(2)806 5152 y Fz(\))851 5089 y Fi(1)p 851 5101 31 3 v 851 5143 a(4)905 5067 y Fs(f)1211 5006 y Fz(1)p 970 5046 529 4 v 970 5152 a(\()p Fq(j)p Fs(D)1105 5166 y Fr(0)1145 5152 y Fq(j)1170 5126 y Fr(2)1230 5152 y Fz(+)g Fs(\021)1369 5126 y Fr(2)1409 5152 y Fz(\))1454 5089 y Fi(1)p 1454 5101 31 3 v 1454 5143 a(4)1508 4908 y Fp(\014)1508 4963 y(\014)1508 5017 y(\014)1508 5072 y(\014)1508 5126 y(\014)1524 4908 y(\014)1524 4963 y(\014)1524 5017 y(\014)1524 5072 y(\014)1524 5126 y(\014)1554 5185 y Fd(S)1611 5194 y Fi(6)1733 5067 y Fq(\024)1887 4908 y Fp(\014)1887 4963 y(\014)1887 5017 y(\014)1887 5072 y(\014)1887 5126 y(\014)1902 4908 y(\014)1902 4963 y(\014)1902 5017 y(\014)1902 5072 y(\014)1902 5126 y(\014)2184 5006 y Fz(1)p 1942 5046 529 4 v 1942 5152 a(\()p Fq(j)p Fs(D)2077 5166 y Fr(0)2117 5152 y Fq(j)2142 5126 y Fr(2)2202 5152 y Fz(+)g Fs(\021)2341 5126 y Fr(2)2381 5152 y Fz(\))2426 5089 y Fi(1)p 2426 5101 31 3 v 2426 5143 a(4)2481 5067 y Fq(j)p Fs(f)10 b Fq(j)2586 5030 y Fr(1)p Fo(=)p Fr(2)2696 4908 y Fp(\014)2696 4963 y(\014)2696 5017 y(\014)2696 5072 y(\014)2696 5126 y(\014)2711 4908 y(\014)2711 4963 y(\014)2711 5017 y(\014)2711 5072 y(\014)2711 5126 y(\014)2741 4934 y Fr(2)2741 5185 y Fd(S)2798 5194 y Fi(12)1733 5383 y Fq(\024)83 b Fz(\(2)p Fs(\031)s Fz(\))2057 5345 y FA(\000)p Fr(1)p Fo(=)p Fr(2)2238 5255 y Fp(\022)2305 5259 y(Z)2355 5465 y Fj(R)2403 5446 y Fi(3)2704 5321 y Fs(du)p 2467 5362 573 4 v 2467 5445 a Fz(1)21 b(+)f Fq(j)p Fs(u)p Fq(j)2726 5419 y Fr(2)2786 5445 y Fz(+)g Fs(\021)2925 5419 y Fr(2)2965 5445 y Fz(\))3000 5419 y Fr(3)3049 5255 y Fp(\023)3116 5277 y Fr(1)p Fo(=)p Fr(6)3241 5383 y Fq(j)-14 b(j)p Fs(f)10 b Fq(j)-16 b(j)3366 5410 y Fo(L)3414 5391 y Fi(6)1733 5626 y Fz(=)2050 5565 y Fs(S)2106 5579 y Fr(6)p 1897 5605 402 4 v 1897 5692 a Fz(4)p Fs(\031)s(E)5 b Fz(\()p Fs(\021)s Fz(\))2187 5666 y Fr(1)p Fo(=)p Fr(2)2324 5626 y Fq(j)-15 b(j)p Fs(f)10 b Fq(j)-16 b(j)2449 5653 y Fo(L)2497 5634 y Fi(6)2551 5626 y Fs(:)1844 5906 y Fz(24)p eop end %%Page: 25 25 TeXDict begin 25 24 bop 0 63 a Fz(Finally)31 b(since)1289 188 y Fq(j)-15 b(j)q Fs(f)10 b Fq(j)-16 b(j)1414 215 y Fo(L)1462 196 y Fi(6)1526 188 y Fq(\024)25 b Fs(C)1687 202 y Fr(6)1742 188 y Fq(j)-15 b(jr)p Fs(f)10 b Fq(j)-16 b(j)1943 215 y Fo(L)1991 196 y Fi(2)2055 188 y Fz(=)25 b Fs(C)2216 202 y Fr(6)2255 188 y Fq(j)-15 b(j)p Fs(')2349 150 y FA(0)2373 188 y Fq(j)g(j)2408 202 y FA(Y)2465 188 y Fs(;)1128 b Fz(\(46\))0 368 y(and)30 b Fq(j)-15 b(j)p Fs(')271 335 y FA(0)295 368 y Fq(j)g(j)330 382 y FA(Y)412 368 y Fz(=)25 b(\(4)p Fs(\031)s Fz(\))p Fq(j)-15 b(j)p Fs(\032)760 335 y FA(0)785 368 y Fq(j)g(j)820 382 y FA(C)865 368 y Fz(,)31 b(w)m(e)g(obtain)1066 640 y Fq(j)-15 b(j)p Fs(Q)1173 602 y FA(0)1173 662 y Fr(1)p Fo(;)p Fr(1)1267 640 y Fq(j)g(j)1302 654 y FA(Q)1390 640 y Fq(\024)1496 578 y Fz(4)p Fs(S)1597 592 y Fr(6)1636 578 y Fs(C)1701 592 y Fr(6)p 1496 619 246 4 v 1568 702 a Fz(2)p Fs(\031)1766 516 y Fp(Z)1857 542 y Fr(+)p FA(1)1816 722 y(\0001)2114 578 y Fs(d\021)p 2011 619 302 4 v 2011 706 a(E)5 b Fz(\()p Fs(\021)s Fz(\))2201 680 y Fr(3)p Fo(=)p Fr(2)2323 640 y Fq(j)-15 b(j)p Fs(R)q Fq(j)g(j)2463 654 y FA(R)2528 640 y Fq(j)g(j)p Fs(\032)2610 602 y FA(0)2633 640 y Fq(j)g(j)2668 654 y FA(C)0 904 y Fz(and)1195 1028 y Fq(j)g(j)p Fs(Q)1302 1042 y Fr(1)p Fo(;)p Fr(1)1396 1028 y Fq(j)g(j)1431 1042 y FA(Q)1518 1028 y Fq(\024)25 b Fz(8)p Fs(S)1715 1042 y Fr(6)1755 1028 y Fs(C)1820 1042 y Fr(6)1859 1028 y Fs(K)1936 1047 y Fr(3)p Fo(=)p Fr(2)2047 1028 y Fs(C)2112 1042 y Fo(R)2169 1028 y Fq(j)-15 b(j)p Fs(Q)p Fq(j)g(j)2311 1042 y FA(Q)2374 1028 y Fq(j)g(j)p Fs(\032)2456 991 y FA(0)2479 1028 y Fq(j)g(j)2514 1042 y FA(C)2560 1028 y Fs(:)0 1328 y Fq(\017)58 b Fs(Q)175 1342 y Fr(0)p Fo(;)p Fr(2)269 1328 y Fz(.)41 b(Unfortunately)-8 b(,)30 b(the)f(metho)s(d)f (used)g(ab)s(o)m(v)m(e)j(cannot)e(b)s(e)f(applied)h(to)h Fs(Q)2804 1342 y Fr(0)p Fo(;)p Fr(2)2898 1328 y Fz(.)40 b(In)28 b(this)h(case,)i(w)m(e)e(ha)m(v)m(e)0 1441 y(to)i(calculate)i (this)d(term)h(explicitely)-8 b(.)43 b(W)-8 b(e)31 b(can)g(write)1405 1665 y Fs(Q)1477 1679 y Fr(0)p Fo(;)p Fr(2)1597 1665 y Fz(=)1828 1579 y Fp(X)1693 1780 y Fo(\017)1722 1789 y Fi(1)1756 1780 y Fo(;\017)1805 1789 y Fi(2)1839 1780 y Fo(;\017)1888 1789 y Fi(3)1921 1780 y FA(2f\006g)2109 1665 y Fs(Q)2181 1624 y Fo(\017)2210 1633 y Fi(1)2244 1624 y Fo(\017)2273 1633 y Fi(2)2307 1624 y Fo(\017)2336 1633 y Fi(3)2181 1691 y Fr(0)p Fo(;)p Fr(2)0 1985 y Fz(where)f(for)g (instance)h(\(b)m(y)g(a)f(residuum)f(form)m(ula\))1306 2194 y Fm(\\)1292 2230 y Fs(Q)1364 2192 y Fr(+++)1364 2256 y(0)p Fo(;)p Fr(2)1533 2230 y Fz(\()p Fs(p;)15 b(q)s Fz(\))25 b(=)1869 2194 y Fm(\\)1854 2230 y Fs(Q)1926 2192 y FA(\000\000\000)1926 2256 y Fr(0)p Fo(;)p Fr(2)2095 2230 y Fz(\()p Fs(p;)15 b(q)s Fz(\))26 b(=)f(0)p Fs(;)546 2507 y Fm(\\)532 2543 y Fs(Q)604 2505 y Fr(+)p FA(\000\000)604 2569 y Fr(0)p Fo(;)p Fr(2)773 2543 y Fz(\()p Fs(p;)15 b(q)s Fz(\))25 b(=)g(\(2)p Fs(\031)s Fz(\))1264 2506 y FA(\000)p Fr(3)1375 2420 y Fp(Z)1426 2626 y Fj(R)1474 2607 y Fi(3)1528 2543 y Fs(dp)1621 2557 y Fr(1)1670 2482 y Fz(\003)1733 2449 y Fr(+)1792 2482 y Fz(\()p Fs(p)p Fz(\))1925 2458 y Fp(b)1908 2482 y Fs(')1967 2456 y FA(0)1991 2482 y Fz(\()p Fs(p)c Fq(\000)f Fs(p)2230 2496 y Fr(1)2269 2482 y Fz(\)\003)2367 2449 y FA(\000)2426 2482 y Fz(\()p Fs(p)2507 2496 y Fr(1)2547 2482 y Fz(\))2598 2458 y Fp(b)2582 2482 y Fs(')2641 2456 y FA(0)2665 2482 y Fz(\()p Fs(p)2746 2496 y Fr(1)2806 2482 y Fq(\000)g Fs(q)s Fz(\)\003)3039 2449 y FA(\000)3098 2482 y Fz(\()p Fs(q)s Fz(\))p 1670 2522 1543 4 v 1863 2606 a(\()p Fs(E)5 b Fz(\()p Fs(p)p Fz(\))21 b(+)f Fs(E)5 b Fz(\()p Fs(q)s Fz(\)\)\()p Fs(E)g Fz(\()p Fs(p)p Fz(\))23 b(+)d Fs(E)5 b Fz(\()p Fs(p)2909 2620 y Fr(1)2949 2606 y Fz(\)\))3222 2543 y Fs(;)546 2831 y Fm(\\)532 2867 y Fs(Q)604 2829 y Fr(+)p FA(\000)p Fr(+)604 2893 y(0)p Fo(;)p Fr(2)773 2867 y Fz(\()p Fs(p;)15 b(q)s Fz(\))25 b(=)g(\(2)p Fs(\031)s Fz(\))1264 2830 y FA(\000)p Fr(3)1375 2743 y Fp(Z)1426 2950 y Fj(R)1474 2931 y Fi(3)1528 2867 y Fs(dp)1621 2881 y Fr(1)1670 2806 y Fz(\003)1733 2773 y Fr(+)1792 2806 y Fz(\()p Fs(p)p Fz(\))1925 2782 y Fp(b)1908 2806 y Fs(')1967 2779 y FA(0)1991 2806 y Fz(\()p Fs(p)c Fq(\000)f Fs(p)2230 2820 y Fr(1)2269 2806 y Fz(\)\003)2367 2773 y FA(\000)2426 2806 y Fz(\()p Fs(p)2507 2820 y Fr(1)2547 2806 y Fz(\))2598 2782 y Fp(b)2582 2806 y Fs(')2641 2779 y FA(0)2665 2806 y Fz(\()p Fs(p)2746 2820 y Fr(1)2806 2806 y Fq(\000)g Fs(q)s Fz(\)\003)3039 2773 y Fr(+)3098 2806 y Fz(\()p Fs(q)s Fz(\))p 1670 2846 V 1843 2930 a(\()p Fs(E)5 b Fz(\()p Fs(p)p Fz(\))22 b(+)e Fs(E)5 b Fz(\()p Fs(p)2332 2944 y Fr(1)2371 2930 y Fz(\)\)\()p Fs(E)g Fz(\()p Fs(q)s Fz(\))23 b(+)d Fs(E)5 b Fz(\()p Fs(p)2929 2944 y Fr(1)2968 2930 y Fz(\)\))3222 2867 y Fs(;)0 3139 y Fz(and)36 b(similar)i(form)m(ulas)f(for)f(the)h(other)h Fs(Q)1490 3099 y Fo(\017)1519 3108 y Fi(1)1553 3099 y Fo(\017)1582 3108 y Fi(2)1616 3099 y Fo(\017)1645 3108 y Fi(3)1490 3165 y Fr(0)p Fo(;)p Fr(2)1683 3139 y Fz(.)60 b(W)-8 b(e)38 b(no)m(w)f(treat)h(for)f(instance)2877 3103 y Fm(\\)2863 3139 y Fs(Q)2935 3101 y Fr(+)p FA(\000\000)2935 3165 y Fr(0)p Fo(;)p Fr(2)3103 3139 y Fz(.)61 b(Using)37 b(\(20\),)j(w)m(e)0 3252 y(ma)m(y)31 b(obtain)83 3536 y Fs(E)5 b Fz(\()p Fs(p)21 b Fq(\000)f Fs(q)s Fz(\))p Fs(E)5 b Fz(\()p Fs(p)20 b Fz(+)g Fs(q)s Fz(\))770 3498 y Fr(1)p Fo(=)p Fr(2)881 3536 y Fq(j)920 3500 y Fm(\\)906 3536 y Fs(Q)978 3498 y Fr(+)p FA(\000\000)978 3562 y Fr(0)p Fo(;)p Fr(2)1146 3536 y Fq(j)26 b(\024)f Fz(2\(2)p Fs(\031)s Fz(\))1508 3498 y FA(\000)p Fr(3)1619 3412 y Fp(Z)1670 3618 y Fj(R)1718 3599 y Fi(3)1787 3536 y Fs(dp)1880 3550 y Fr(1)1984 3474 y Fs(E)5 b Fz(\()p Fs(p)21 b Fq(\000)f Fs(p)2295 3488 y Fr(1)2334 3474 y Fz(\))p 1929 3515 496 4 v 1929 3602 a Fs(E)5 b Fz(\()p Fs(p)21 b Fz(+)f Fs(p)2240 3616 y Fr(1)2279 3602 y Fz(\))2314 3576 y Fr(2)p Fo(=)p Fr(3)2434 3536 y Fq(\002)1517 3809 y(\002)1608 3705 y Fp(\014)1608 3759 y(\014)1608 3814 y(\014)1638 3809 y Fz(\003)1701 3772 y Fr(+)1760 3809 y Fz(\()p Fs(p)p Fz(\))1893 3785 y Fp(b)1876 3809 y Fs(')1935 3783 y FA(0)1959 3809 y Fz(\()p Fs(p)h Fq(\000)f Fs(p)2198 3823 y Fr(1)2237 3809 y Fz(\)\003)2335 3772 y FA(\000)2394 3809 y Fz(\()p Fs(p)2475 3823 y Fr(1)2515 3809 y Fz(\))2550 3705 y Fp(\014)2550 3759 y(\014)2550 3814 y(\014)2601 3809 y Fq(\002)2702 3748 y Fs(E)5 b Fz(\()p Fs(p)2855 3762 y Fr(1)2915 3748 y Fq(\000)19 b Fs(q)s Fz(\))p Fq(j)3126 3724 y Fp(b)3109 3748 y Fs(')3168 3721 y FA(0)3193 3748 y Fz(\()p Fs(p)3274 3762 y Fr(1)3333 3748 y Fq(\000)h Fs(q)s Fz(\))p Fq(j)p 2702 3788 828 4 v 2798 3875 a Fs(E)5 b Fz(\()p Fs(p)2951 3889 y Fr(1)2990 3875 y Fz(\))3025 3849 y Fr(1)p Fo(=)p Fr(3)3136 3875 y Fs(E)g Fz(\()p Fs(q)s Fz(\))3322 3849 y Fr(1)p Fo(=)p Fr(2)3539 3809 y Fs(dp)3632 3823 y Fr(1)3671 3809 y Fs(:)0 4072 y Fz(So,)31 b(w)m(e)f(ma)m(y)h(write)430 4332 y Fq(j)-15 b(j)p Fs(Q)537 4294 y Fr(+)p FA(\000\000)537 4358 y Fr(0)p Fo(;)p Fr(2)706 4332 y Fq(j)g(j)741 4346 y FA(Q)829 4332 y Fq(\024)25 b Fz(2)985 4200 y Fp(\014)985 4255 y(\014)985 4310 y(\014)985 4364 y(\014)1000 4200 y(\014)1000 4255 y(\014)1000 4310 y(\014)1000 4364 y(\014)1031 4332 y Fs(M)1119 4347 y Fo(f)1289 4271 y Fz(1)p 1174 4311 276 4 v 1174 4399 a Fq(j)p Fs(D)1274 4413 y Fr(0)1314 4399 y Fq(j)1339 4372 y Fr(1)p Fo(=)p Fr(3)1459 4332 y Fs(f)1638 4271 y Fz(1)p 1524 4311 V 1524 4399 a Fq(j)p Fs(D)1624 4413 y Fr(0)1664 4399 y Fq(j)1689 4372 y Fr(1)p Fo(=)p Fr(2)1809 4200 y Fp(\014)1809 4255 y(\014)1809 4310 y(\014)1809 4364 y(\014)1824 4200 y(\014)1824 4255 y(\014)1824 4310 y(\014)1824 4364 y(\014)1854 4425 y Fd(S)1911 4434 y Fi(2)1975 4332 y Fq(\024)g Fz(2)15 b Fq(j)-14 b(j)p Fs(M)2255 4347 y Fo(f)2301 4332 y Fq(j)f(j)2336 4364 y Fd(S)2393 4373 y Fi(2)2447 4200 y Fp(\014)2447 4255 y(\014)2447 4310 y(\014)2447 4364 y(\014)2462 4200 y(\014)2462 4255 y(\014)2462 4310 y(\014)2462 4364 y(\014)2617 4271 y Fz(1)p 2503 4311 V 2503 4399 a Fq(j)p Fs(D)2603 4413 y Fr(0)2643 4399 y Fq(j)2668 4372 y Fr(1)p Fo(=)p Fr(3)2788 4332 y Fs(f)2967 4271 y Fz(1)p 2852 4311 V 2852 4399 a Fq(j)p Fs(D)2952 4413 y Fr(0)2992 4399 y Fq(j)3017 4372 y Fr(1)p Fo(=)p Fr(2)3137 4200 y Fp(\014)3137 4255 y(\014)3137 4310 y(\014)3137 4364 y(\014)3152 4200 y(\014)3152 4255 y(\014)3152 4310 y(\014)3152 4364 y(\014)3183 4425 y Fd(S)3240 4433 y Fl(1)3324 4332 y Fs(;)0 4609 y Fz(where)1027 4757 y Fp(d)1025 4780 y Fs(M)1113 4795 y Fo(f)1159 4780 y Fz(\()p Fs(p;)15 b(q)s Fz(\))26 b(:=)f(\(2)p Fs(\031)s Fz(\))1676 4743 y FA(\000)p Fr(3)p Fo(=)p Fr(2)1869 4695 y Fp(b)1852 4719 y Fs(f)10 b Fz(\()p Fs(p)20 b Fq(\000)g Fs(q)s Fz(\))15 b Fq(j)p Fz(\003)2281 4686 y Fr(+)2340 4719 y Fz(\()p Fs(p)p Fz(\)\003)2519 4686 y FA(\000)2579 4719 y Fz(\()p Fs(q)s Fz(\))p Fq(j)p 1852 4759 867 4 v 2059 4846 a Fs(E)5 b Fz(\()p Fs(p)20 b Fz(+)g Fs(q)s Fz(\))2402 4820 y Fr(2)p Fo(=)p Fr(3)2729 4780 y Fs(:)864 b Fz(\(47\))0 5036 y Fe(Lemma)35 b(12.)42 b Fy(When)33 b Fs(M)897 5051 y Fo(f)975 5036 y Fy(is)f(de\014ne)-5 b(d)34 b(by)e(formula)i Fz(\(47\))p Fy(,)g(then)1140 5330 y Fq(j)-15 b(j)p Fs(M)1263 5345 y Fo(f)1309 5330 y Fq(j)g(j)1344 5362 y Fd(S)1401 5371 y Fi(2)1465 5330 y Fq(\024)1571 5269 y Fs(C)1636 5283 y Fo(M)p 1571 5309 144 4 v 1593 5393 a Fz(4)p Fs(\031)1740 5202 y Fp(\022)1807 5206 y(Z)1858 5413 y Fj(R)1906 5394 y Fi(3)1960 5330 y Fq(j)p Fs(k)s Fq(j)2060 5293 y Fr(2)2100 5330 y Fq(j)2142 5306 y Fp(b)2125 5330 y Fs(f)9 b Fz(\()p Fs(k)s Fz(\))p Fq(j)2324 5293 y Fr(2)2365 5330 y Fs(dk)2462 5202 y Fp(\023)2529 5225 y Fr(1)p Fo(=)p Fr(2)0 5656 y Fy(wher)-5 b(e)34 b Fs(C)322 5670 y Fo(M)426 5656 y Fz(:=)25 b(2)607 5555 y Fp(\020)662 5583 y(R)723 5609 y FA(1)705 5688 y Fr(0)975 5620 y Fo(t)1000 5597 y Fi(2)1047 5620 y Fo(dt)p 822 5635 439 4 v 822 5696 a(E)t Fr(\(2)p Fo(t)p Fr(\))992 5676 y Fi(4)p Fg(=)p Fi(3)1090 5696 y Fo(E)t Fr(\()p Fo(t)p Fr(\))1225 5677 y Fi(2)1271 5555 y Fp(\021)1325 5578 y Fr(1)p Fo(=)p Fr(2)1460 5656 y Fq(')g Fz(2)p Fs(:)p Fz(1589)p Fy(.)1844 5906 y Fz(25)p eop end %%Page: 26 26 TeXDict begin 26 25 bop 141 90 a Fy(Pr)-5 b(o)g(of)34 b({)63 b Fz(W)-8 b(e)32 b(ha)m(v)m(e)g Fq(j)p Fz(\003)949 57 y Fr(+)1008 90 y Fz(\()p Fs(p)p Fz(\)\003)1187 57 y FA(\000)1247 90 y Fz(\()p Fs(q)s Fz(\))p Fq(j)1386 43 y Fr(2)1451 90 y Fz(=)25 b(T)-8 b(r)1641 109 y Fj(C)1689 90 y Fi(4)24 b Fz(\(\003)1841 57 y Fr(+)1900 90 y Fz(\()p Fs(p)p 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Fr(2)2329 466 y Fp(Z)2711 529 y Fs(du)p 2445 569 631 4 v 2445 656 a Fz(2)p Fs(E)c Fz(\(2)p Fs(u)p Fz(\))2729 630 y Fr(4)p Fo(=)p Fr(3)2841 656 y Fs(E)g Fz(\()p Fs(u)p Fz(\))3035 630 y Fr(2)1271 850 y Fq(\024)82 b Fz(\(2)p Fs(\031)s Fz(\))1594 812 y FA(\000)p Fr(2)1705 721 y Fp(\022)1772 726 y(Z)1878 850 y Fs(dk)s Fq(j)p Fs(k)s Fq(j)2075 812 y Fr(2)2116 850 y Fq(j)2158 826 y Fp(b)2141 850 y Fs(f)9 b Fz(\()p Fs(k)s Fz(\))p Fq(j)2340 812 y Fr(2)2381 721 y Fp(\023)2463 726 y(Z)2554 752 y FA(1)2513 932 y Fr(0)2843 788 y Fs(t)2876 755 y Fr(2)2931 788 y Fs(dt)p 2654 829 547 4 v 2654 916 a(E)c Fz(\(2)p Fs(t)p Fz(\))2874 889 y Fr(4)p Fo(=)p Fr(3)2985 916 y Fs(E)g Fz(\()p Fs(t)p Fz(\))3160 890 y Fr(2)3210 850 y Fs(:)p 3331 850 4 62 v 3335 792 55 4 v 3335 850 V 3389 850 4 62 v 141 1087 a Fz(Finally)-8 b(,)32 b(since)f(b)m(y)f(\(46\))703 1189 y Fp(\014)703 1244 y(\014)703 1298 y(\014)703 1353 y(\014)718 1189 y(\014)718 1244 y(\014)718 1298 y(\014)718 1353 y(\014)874 1260 y Fz(1)p 759 1300 276 4 v 759 1387 a Fq(j)p Fs(D)859 1401 y Fr(0)899 1387 y Fq(j)924 1361 y Fr(1)p Fo(=)p Fr(3)1044 1321 y Fs(f)1223 1260 y Fz(1)p 1108 1300 V 1108 1387 a Fq(j)p Fs(D)1208 1401 y Fr(0)1248 1387 y Fq(j)1273 1361 y Fr(1)p Fo(=)p Fr(2)1393 1189 y Fp(\014)1393 1244 y(\014)1393 1298 y(\014)1393 1353 y(\014)1409 1189 y(\014)1409 1244 y(\014)1409 1298 y(\014)1409 1353 y(\014)1439 1414 y Fd(S)1496 1422 y Fl(1)1590 1321 y Fq(\024)1686 1189 y Fp(\014)1686 1244 y(\014)1686 1298 y(\014)1686 1353 y(\014)1701 1189 y(\014)1701 1244 y(\014)1701 1298 y(\014)1701 1353 y(\014)1857 1260 y Fz(1)p 1742 1300 V 1742 1387 a Fq(j)p Fs(D)1842 1401 y Fr(0)1882 1387 y Fq(j)1907 1361 y Fr(1)p Fo(=)p Fr(3)2027 1321 y Fs(f)2206 1260 y Fz(1)p 2091 1300 V 2091 1387 a Fq(j)p Fs(D)2191 1401 y Fr(0)2231 1387 y Fq(j)2256 1361 y Fr(1)p Fo(=)p Fr(2)2376 1189 y Fp(\014)2376 1244 y(\014)2376 1298 y(\014)2376 1353 y(\014)2392 1189 y(\014)2392 1244 y(\014)2392 1298 y(\014)2392 1353 y(\014)2422 1414 y Fd(S)2479 1423 y Fi(6)2543 1321 y Fq(\024)2649 1259 y Fs(S)2705 1273 y Fr(6)p Fo(;)p Fr(5)p 2649 1300 151 4 v 2674 1384 a Fz(4)p Fs(\031)2824 1321 y Fq(j)-15 b(j)p Fs(f)10 b Fq(j)-15 b(j)2949 1348 y Fo(L)2997 1329 y Fi(6)3051 1321 y Fs(;)0 1567 y Fz(w)m(e)31 b(obtain)1315 1679 y Fq(j)-15 b(j)p Fs(Q)1422 1641 y Fr(+)p FA(\000\000)1422 1705 y Fr(0)p Fo(;)p Fr(2)1591 1679 y Fq(j)g(j)1626 1693 y FA(Q)1713 1679 y Fq(\024)25 b Fz(2)p Fs(S)1910 1693 y Fr(6)p Fo(;)p Fr(5)2005 1679 y Fs(C)2070 1693 y Fo(M)2149 1679 y Fs(C)2214 1693 y Fr(6)2253 1679 y Fq(j)-15 b(j)p Fs(\032)2335 1642 y FA(0)2359 1679 y Fq(j)g(j)2394 1642 y Fr(2)2394 1702 y FA(C)2439 1679 y Fs(:)0 1836 y Fz(This)30 b(result)g(is)g(immediatly)i(extended)e(to)h(the)g(others)f(terms)g (and)g(since)h(w)m(e)g(can)f(pro)m(v)m(e)556 2021 y Fq(j)p Fs(Q)p Fq(j)678 1983 y Fr(2)743 2021 y Fz(=)25 b Fq(j)p Fs(Q)936 1983 y Fr(++)p FA(\000)1125 2021 y Fz(+)20 b Fs(Q)1288 1983 y Fr(+)p FA(\000\000)1457 2021 y Fq(j)1482 1983 y Fr(2)1542 2021 y Fz(+)f Fq(j)p Fs(Q)1729 1983 y FA(\000)p Fr(++)1919 2021 y Fz(+)h Fs(Q)2082 1983 y FA(\000\000)p Fr(+)2250 2021 y Fq(j)2275 1983 y Fr(2)2335 2021 y Fz(+)g Fq(j)p Fs(Q)2523 1983 y Fr(+)p FA(\000)p Fr(+)2692 2021 y Fq(j)2717 1983 y Fr(2)2777 2021 y Fz(+)g Fq(j)p Fs(Q)2965 1983 y FA(\000)p Fr(+)p FA(\000)3134 2021 y Fq(j)3159 1983 y Fr(2)3198 2021 y Fs(;)0 2206 y Fz(w)m(e)31 b(arriv)m(e)g(at)1269 2318 y Fq(j)-15 b(j)p Fs(Q)1376 2332 y Fr(0)p Fo(;)p Fr(2)1470 2318 y Fq(j)g(j)1505 2332 y FA(Q)1593 2318 y Fq(\024)25 b Fz(2)1734 2239 y Fq(p)p 1810 2239 91 4 v 79 x Fz(10)q Fs(S)1957 2332 y Fr(6)p Fo(;)p Fr(5)2051 2318 y Fs(C)2116 2332 y Fo(M)2195 2318 y Fs(C)2260 2332 y Fr(6)2299 2318 y Fq(j)-15 b(j)p Fs(\032)2381 2281 y FA(0)2405 2318 y Fq(j)g(j)2440 2281 y Fr(2)2440 2341 y FA(C)2485 2318 y Fs(:)141 2562 y Fe(Step)41 b(2)h(:)59 b(Estimates)41 b(on)h(the)f(densit)m(y)g Fs(\032)1813 2576 y Fr(2)1853 2562 y Fe(.)57 b Fz(Let)37 b(us)e(no)m(w)h(treat)h (the)g(densit)m(y)f Fs(\032)3182 2576 y Fr(2)3221 2562 y Fz(.)58 b(The)35 b(general)0 2675 y(idea)c(of)f(the)h(pro)s(of)f(is)g (to)h(estimate)h Fq(h)p Fs(\032)1338 2689 y Fr(2)1378 2675 y Fs(;)15 b(\020)7 b Fq(i)31 b Fz(in)f(terms)g(of)h(the)f(norm)g Fq(j)-15 b(j)p Fs(\020)7 b Fq(j)-15 b(j)2505 2690 y FA(C)2546 2671 y Fl(0)2603 2675 y Fz(b)m(y)30 b(using)353 2909 y Fq(jh)p Fs(\032;)15 b(\020)7 b Fq(i)q(j)26 b Fz(=)f Fq(j)p Fz(T)-8 b(r)15 b(\()p Fs(Q\020)7 b Fz(\))p Fq(j)25 b Fz(=)1199 2805 y Fp(\014)1199 2859 y(\014)1199 2914 y(\014)1229 2909 y Fz(T)-8 b(r)1338 2808 y Fp(\020)1406 2885 y(c)1393 2909 y Fs(Q\020)1511 2808 y Fp(\021)1565 2805 y(\014)1565 2859 y(\014)1565 2914 y(\014)1621 2909 y Fz(=)1717 2778 y Fp(\014)1717 2832 y(\014)1717 2887 y(\014)1717 2941 y(\014)1747 2786 y(Z)1798 2992 y Fj(R)1846 2973 y Fi(3)1899 2909 y Fz(T)g(r)1993 2929 y Fj(C)2041 2910 y Fi(4)2095 2808 y Fp(\020)2163 2885 y(c)2149 2909 y Fs(Q\020)2268 2808 y Fp(\021)2322 2909 y Fz(\()p Fs(p;)15 b(p)p Fz(\))g Fs(dp)2632 2778 y Fp(\014)2632 2832 y(\014)2632 2887 y(\014)2632 2941 y(\014)2688 2909 y Fq(\024)2784 2786 y Fp(Z)2835 2992 y Fj(R)2883 2973 y Fi(3)2937 2909 y Fq(j)2976 2885 y Fp(c)2962 2909 y Fs(Q\020)6 b Fz(\()p Fs(p;)15 b(p)p Fz(\))p Fq(j)p Fs(dp:)0 3139 y Fz(This)30 b(can)g(b)s(e)g(done)g(if)g(w)m(e)h(kno)m(w)g(that)g Fs(Q\020)g Fq(2)25 b Fh(S)1671 3153 y Fr(1)1711 3139 y Fz(.)41 b(But)30 b(w)m(e)h(ha)m(v)m(e)258 3368 y Fq(j)-15 b(j)q Fs(Q\020)7 b Fq(j)-16 b(j)447 3395 y Fd(S)504 3404 y Fi(1)568 3368 y Fz(=)664 3236 y Fp(\014)664 3291 y(\014)664 3345 y(\014)664 3400 y(\014)680 3236 y(\014)680 3291 y(\014)680 3345 y(\014)680 3400 y(\014)710 3368 y Fs(Q)p Fq(j)p Fs(D)882 3382 y Fr(0)922 3368 y Fq(j)947 3331 y Fr(2)1076 3307 y Fz(1)p 996 3347 205 4 v 996 3431 a Fq(j)p Fs(D)1096 3445 y Fr(0)1136 3431 y Fq(j)1161 3404 y Fr(2)1211 3368 y Fs(\020)1258 3236 y Fp(\014)1258 3291 y(\014)1258 3345 y(\014)1258 3400 y(\014)1273 3236 y(\014)1273 3291 y(\014)1273 3345 y(\014)1273 3400 y(\014)1303 3459 y Fd(S)1360 3468 y Fi(1)1424 3368 y Fq(\024)1520 3291 y Fp(\014)1520 3345 y(\014)1535 3291 y(\014)1535 3345 y(\014)1565 3368 y Fs(Q)p Fq(j)p Fs(D)1737 3382 y Fr(0)1777 3368 y Fq(j)1802 3331 y Fr(2)1842 3291 y Fp(\014)1842 3345 y(\014)1857 3291 y(\014)1857 3345 y(\014)1887 3404 y Fd(S)1944 3413 y Fi(2)1998 3236 y Fp(\014)1998 3291 y(\014)1998 3345 y(\014)1998 3400 y(\014)2014 3236 y(\014)2014 3291 y(\014)2014 3345 y(\014)2014 3400 y(\014)2133 3307 y Fz(1)p 2054 3347 V 2054 3431 a Fq(j)p Fs(D)2154 3445 y Fr(0)2194 3431 y Fq(j)2219 3404 y Fr(2)2268 3368 y Fs(\020)2315 3236 y Fp(\014)2315 3291 y(\014)2315 3345 y(\014)2315 3400 y(\014)2330 3236 y(\014)2330 3291 y(\014)2330 3345 y(\014)2330 3400 y(\014)2360 3459 y Fd(S)2417 3468 y Fi(2)2481 3368 y Fq(\024)25 b Fs(E)5 b Fz(\(\003\))2782 3331 y Fr(2)2838 3368 y Fq(j)-15 b(j)q Fs(Q)p Fq(j)g(j)2981 3395 y Fd(S)3038 3404 y Fi(2)3102 3306 y Fs(S)3158 3320 y Fr(2)p Fo(;)p Fr(4)p 3102 3347 151 4 v 3127 3431 a Fz(4)p Fs(\031)3277 3368 y Fq(j)g(j)p Fs(\020)7 b Fq(j)-15 b(j)3394 3395 y Fo(L)3442 3376 y Fi(2)3496 3368 y Fs(;)0 3624 y Fz(sho)m(wing)31 b(that)h Fs(Q\020)h Fq(2)26 b Fh(S)852 3638 y Fr(1)923 3624 y Fz(when)k Fs(\020)j Fq(2)26 b Fs(L)1383 3591 y Fr(2)1422 3624 y Fz(.)43 b(So,)31 b(in)g(what)g(follo)m(ws,)i(w)m(e)e(shall)h(assume)f(that)g Fs(\020)i Fq(2)26 b(C)3375 3591 y FA(0)3419 3624 y Fq(\\)21 b Fs(L)3563 3591 y Fr(2)3633 3624 y Fz(and)0 3737 y(pro)m(v)m(e)28 b(a)f(b)s(ound)e(dep)s(ending)g(only)i(on)g Fq(j)-15 b(j)p Fs(\020)7 b Fq(j)-15 b(j)1460 3752 y FA(C)1501 3733 y Fl(0)1528 3737 y Fz(.)39 b(By)28 b(the)f(densit)m(y)g(of)g Fq(C)2348 3704 y FA(0)2385 3737 y Fq(\\)13 b Fs(L)2521 3704 y Fr(2)2587 3737 y Fz(in)26 b Fq(C)2742 3704 y FA(0)2766 3737 y Fz(,)i(this)e(will)i(giv)m(e)g(us)e(a)i(b)s(ound)0 3849 y(on)i Fq(j)-15 b(j)p Fs(\032)p Fq(j)g(j)243 3863 y FA(C)289 3849 y Fz(.)141 4075 y(Let)31 b(us)f(remark)g(\014rst)f (that)i Fs(\032)1163 4089 y Fr(0)p Fo(;)p Fr(2)1288 4075 y Fz(v)-5 b(anishes.)40 b(Indeed)30 b(w)m(e)h(ha)m(v)m(e)786 4306 y Fp(d)-136 b Fs(\032)828 4320 y Fr(0)p Fo(;)p Fr(2)922 4306 y Fz(\()p Fs(k)s Fz(\))26 b(=)1292 4244 y(1)p 1174 4285 282 4 v 1174 4372 a(\(2)p Fs(\031)s Fz(\))1344 4345 y Fr(3)p Fo(=)p Fr(2)1480 4182 y Fp(Z)1531 4388 y FA(j)p Fo(p)p FA(j\024)p Fr(\003)1729 4306 y Fz(T)-8 b(r)1822 4325 y Fj(C)1870 4306 y Fi(4)1924 4205 y Fp(\020)1996 4283 y(d)1978 4306 y Fs(Q)2050 4320 y Fr(0)p Fo(;)p Fr(2)2145 4306 y Fz(\()p Fs(p)20 b Fz(+)g Fs(k)s(=)p Fz(2)p Fs(;)15 b(p)21 b Fq(\000)f Fs(k)s(=)p Fz(2\))2850 4205 y Fp(\021)2906 4306 y Fs(dp)0 4548 y Fz(and)83 4790 y(T)-8 b(r)177 4810 y Fj(C)225 4791 y Fi(4)279 4689 y Fp(\020)350 4767 y(d)333 4790 y Fs(Q)405 4804 y Fr(0)p Fo(;)p Fr(2)499 4790 y Fz(\()p Fs(p;)15 b(q)s Fz(\))699 4689 y Fp(\021)779 4790 y Fz(=)968 4729 y(1)p 885 4769 211 4 v 885 4852 a(\(2)p Fs(\031)s Fz(\))1055 4826 y Fr(4)1121 4666 y Fp(Z)1212 4693 y Fr(+)p FA(1)1172 4872 y(\0001)1357 4790 y Fs(d\021)1468 4666 y Fp(Z)1518 4872 y Fj(R)1566 4854 y Fi(3)1635 4790 y Fs(dp)1728 4804 y Fr(1)1768 4790 y Fz(T)-8 b(r)1861 4810 y Fj(C)1909 4791 y Fi(4)1963 4662 y Fp(\022)2228 4729 y Fz(1)p 2040 4769 422 4 v 2040 4852 a Fs(D)2115 4866 y Fr(0)2155 4852 y Fz(\()p Fs(p)p Fz(\))20 b(+)g Fs(i\021)2488 4766 y Fp(b)2472 4790 y Fs(')2531 4764 y FA(0)2555 4790 y Fz(\()p Fs(p)g Fq(\000)g Fs(p)2793 4804 y Fr(1)2832 4790 y Fz(\))p Fq(\002)1176 5044 y(\002)1465 4983 y Fz(1)p 1257 5024 462 4 v 1257 5107 a Fs(D)1332 5121 y Fr(0)1371 5107 y Fz(\()p Fs(p)1452 5121 y Fr(1)1492 5107 y Fz(\))g(+)g Fs(i\021)1744 5020 y Fp(b)1728 5044 y Fs(')1787 5018 y FA(0)1811 5044 y Fz(\()p Fs(p)1892 5058 y Fr(1)1952 5044 y Fq(\000)f Fs(q)s Fz(\))2319 4983 y(1)p 2131 5024 421 4 v 2131 5107 a Fs(D)2206 5121 y Fr(0)2246 5107 y Fz(\()p Fs(q)s Fz(\))i(+)f Fs(i\021)2562 4916 y Fp(\023)567 5315 y Fz(=)756 5254 y(1)p 673 5294 211 4 v 673 5378 a(\(2)p Fs(\031)s Fz(\))843 5351 y Fr(4)909 5191 y Fp(Z)1000 5218 y Fr(+)p FA(1)959 5398 y(\0001)1144 5315 y Fs(d\021)1255 5191 y Fp(Z)1306 5398 y Fj(R)1354 5379 y Fi(3)1423 5315 y Fs(dp)1516 5329 y Fr(1)1983 5230 y Fp(b)1967 5254 y Fs(')2026 5227 y FA(0)2049 5254 y Fz(\()p Fs(p)h Fq(\000)f Fs(p)2288 5268 y Fr(1)2327 5254 y Fz(\))2378 5230 y Fp(b)2362 5254 y Fs(')2421 5227 y FA(0)2445 5254 y Fz(\()p Fs(p)2526 5268 y Fr(1)2586 5254 y Fq(\000)g Fs(q)s Fz(\))p 1565 5294 1592 4 v 1565 5312 a Fp(p)p 1656 5312 428 4 v 79 x Fs(E)5 b Fz(\()p Fs(p)p Fz(\))1844 5364 y Fr(2)1905 5391 y Fz(+)20 b Fs(\021)2044 5364 y Fr(2)2083 5312 y Fp(p)p 2174 5312 467 4 v 79 x Fs(E)5 b Fz(\()p Fs(p)2327 5405 y Fr(1)2367 5391 y Fz(\))2402 5364 y Fr(2)2462 5391 y Fz(+)20 b Fs(\021)2601 5364 y Fr(2)2641 5312 y Fp(p)p 2732 5312 426 4 v 79 x Fs(E)5 b Fz(\()p Fs(q)s Fz(\))2918 5364 y Fr(2)2978 5391 y Fz(+)20 b Fs(\021)3117 5364 y Fr(2)3167 5315 y Fq(\002)1753 5583 y(\002)g Fz(T)-8 b(r)1938 5603 y Fj(C)1986 5584 y Fi(4)2024 5455 y Fp(\024)2072 5583 y Fz(\()p Fs(D)2182 5597 y Fr(0)2222 5583 y Fz(\()p Fs(p)p Fz(\))21 b Fq(\000)f Fs(i\021)s Fz(\)\)\()p Fs(D)2709 5597 y Fr(0)2750 5583 y Fz(\()p Fs(p)2831 5597 y Fr(1)2871 5583 y Fz(\))g Fq(\000)g Fs(i\021)s Fz(\)\()p Fs(D)3241 5597 y Fr(0)3283 5583 y Fz(\()p Fs(q)s Fz(\))g Fq(\000)g Fs(i\021)s Fz(\))3622 5455 y Fp(\025)3671 5583 y Fs(:)1844 5906 y Fz(26)p eop end %%Page: 27 27 TeXDict begin 27 26 bop 0 63 a Fz(No)m(w)32 b(the)g(terms)g(linear)g (in)g(the)f(Dirac)i(matrices)g(are)f(traceless)h(and)f(the)f(remaining) h(terms)g(are)g(o)s(dd)f(in)g Fs(\021)0 176 y Fz(and)i(v)-5 b(anish)33 b(after)h(in)m(tegration.)52 b(This)33 b(can)h(b)s(e)f (easily)h(generalized)i(to)e Fs(\032)2585 191 y Fr(0)p Fo(;)p Fr(2)p Fo(k)2751 176 y Fz(for)f(all)i Fs(k)s Fz(,)g(and)e(is)g (kno)m(wn)g(as)0 289 y Fy(F)-7 b(urry's)34 b(The)-5 b(or)g(em)39 b Fz(in)30 b(the)g(ph)m(ysics)h(litterature.)0 507 y Fq(\017)79 b Fs(\032)171 521 y Fr(2)p Fo(;)p Fr(0)266 507 y Fz(.)68 b(W)-8 b(e)40 b(use)g(here)f(a)h(metho)s(d)f(similar)h (to)g(what)f(w)m(e)h(ha)m(v)m(e)h(done)e(ab)s(o)m(v)m(e.)70 b(W)-8 b(e)40 b(estimate)i(for)d(some)0 620 y Fs(\020)32 b Fq(2)25 b(C)211 587 y FA(0)254 620 y Fq(\\)20 b Fs(L)397 587 y Fr(2)467 620 y Fz(and)29 b Fs(Q)715 635 y Fo(\020)780 620 y Fz(:=)c Fs(Q)973 634 y Fr(2)p Fo(;)p Fr(0)1068 620 y Fs(\020)76 901 y Fq(j)111 878 y Fp(c)101 901 y Fs(Q)173 916 y Fo(\020)213 901 y Fz(\()p Fs(p;)15 b(p)p Fz(\))p Fq(j)84 b(\024)f Fz(\(2)p Fs(\031)s Fz(\))848 864 y FA(\000)p Fr(5)p Fo(=)p Fr(2)1029 778 y Fp(Z)1120 804 y Fr(+)p FA(1)1080 984 y(\0001)1265 901 y Fs(d\021)1376 778 y Fp(Z)9 b(Z)1619 840 y Fq(j)1662 817 y Fp(b)1644 840 y Fs(R)q Fz(\()p Fs(p;)15 b(p)1881 854 y Fr(1)1921 840 y Fz(\))p Fq(j)g(j)2039 817 y Fp(b)2021 840 y Fs(R)r Fz(\()p Fs(p)2173 854 y Fr(1)2212 840 y Fs(;)g(p)2298 854 y Fr(2)2338 840 y Fz(\))p Fq(j)g(j)2444 816 y Fp(b)2438 840 y Fs(\020)7 b Fz(\()p Fs(p)2566 854 y Fr(2)2626 840 y Fq(\000)20 b Fs(p)p Fz(\))p Fq(j)15 b Fs(dp)2931 854 y Fr(1)2986 840 y Fs(dp)3079 854 y Fr(2)p 1552 881 1634 4 v 1552 899 a Fp(p)p 1643 899 428 4 v 78 x Fs(E)5 b Fz(\()p Fs(p)p Fz(\))1831 951 y Fr(2)1892 977 y Fz(+)19 b Fs(\021)2030 951 y Fr(2)2070 899 y Fp(p)p 2161 899 467 4 v 78 x Fs(E)5 b Fz(\()p Fs(p)2314 991 y Fr(1)2354 977 y Fz(\))2389 951 y Fr(2)2449 977 y Fz(+)20 b Fs(\021)2588 951 y Fr(2)2628 899 y Fp(p)p 2719 899 V 78 x Fs(E)5 b Fz(\()p Fs(p)2872 991 y Fr(2)2912 977 y Fz(\))2947 951 y Fr(2)3007 977 y Fz(+)19 b Fs(\021)3145 951 y Fr(2)3195 901 y Fs(;)524 1188 y Fq(\024)83 b Fz(4\(2)p Fs(\031)s Fz(\))893 1150 y FA(\000)p Fr(5)p Fo(=)p Fr(2)1074 1064 y Fp(Z)1165 1090 y Fr(+)p FA(1)1125 1270 y(\0001)1368 1126 y Fs(d\021)p 1320 1167 192 4 v 1320 1250 a(E)5 b Fz(\()p Fs(\021)s Fz(\))1537 1064 y Fp(Z)k(Z)1703 1188 y Fs(dp)1796 1202 y Fr(1)1851 1188 y Fs(dp)1944 1202 y Fr(2)1993 1126 y Fs(E)c Fz(\()p Fs(p)21 b Fq(\000)f Fs(p)2304 1140 y Fr(1)2343 1126 y Fz(\))p Fq(j)2421 1103 y Fp(b)2403 1126 y Fs(R)r Fz(\()p Fs(p;)15 b(p)2641 1140 y Fr(1)2680 1126 y Fz(\))p Fq(j)g Fs(E)5 b Fz(\()p Fs(p)2908 1140 y Fr(1)2969 1126 y Fq(\000)20 b Fs(p)3106 1140 y Fr(2)3145 1126 y Fz(\))p Fq(j)3223 1103 y Fp(b)3205 1126 y Fs(R)q Fz(\()p Fs(p)3356 1140 y Fr(1)3396 1126 y Fs(;)15 b(p)3482 1140 y Fr(2)3522 1126 y Fz(\))p Fq(j)p 1993 1167 1589 4 v 2273 1254 a Fs(E)5 b Fz(\()p Fs(p)21 b Fz(+)f Fs(p)2584 1268 y Fr(1)2623 1254 y Fz(\))2658 1227 y Fr(1)p Fo(=)p Fr(2)2768 1254 y Fs(E)5 b Fz(\()p Fs(p)2921 1268 y Fr(1)2981 1254 y Fz(+)20 b Fs(p)3118 1268 y Fr(2)3157 1254 y Fz(\))3192 1227 y Fr(1)p Fo(=)p Fr(2)3612 1188 y Fq(\002)860 1461 y(\002)1556 1400 y(j)1587 1376 y Fp(b)1581 1400 y Fs(\020)6 b Fz(\()p Fs(p)1708 1414 y Fr(2)1768 1400 y Fq(\000)20 b Fs(p)p Fz(\))p Fq(j)p 941 1440 1641 4 v 941 1527 a Fs(E)5 b Fz(\()p Fs(p)1094 1541 y Fr(2)1153 1527 y Fq(\000)20 b Fs(p)p Fz(\)\()p Fs(E)5 b Fz(\()p Fs(p)p Fz(\))1548 1501 y Fr(2)1609 1527 y Fz(+)20 b Fs(\021)1748 1501 y Fr(2)1788 1527 y Fz(\))1823 1501 y Fr(1)p Fo(=)p Fr(4)1933 1527 y Fz(\()p Fs(E)5 b Fz(\()p Fs(p)2121 1541 y Fr(2)2161 1527 y Fz(\))2196 1501 y Fr(2)2256 1527 y Fz(+)20 b Fs(\021)2395 1501 y Fr(2)2435 1527 y Fz(\))2470 1501 y Fr(1)p Fo(=)p Fr(4)2590 1461 y Fs(;)524 1735 y Fq(\024)83 b Fz(4\(2)p Fs(\031)s Fz(\))893 1697 y FA(\000)p Fr(5)p Fo(=)p Fr(2)1074 1611 y Fp(Z)1165 1637 y Fr(+)p FA(1)1125 1817 y(\0001)1368 1673 y Fs(d\021)p 1320 1714 192 4 v 1320 1797 a(E)5 b Fz(\()p Fs(\021)s Fz(\))1537 1611 y Fp(Z)k(Z)1703 1735 y Fs(dp)1796 1749 y Fr(1)1851 1735 y Fs(dp)1944 1749 y Fr(2)2075 1673 y Fs(R)2145 1640 y FA(0)2168 1673 y Fz(\()p Fs(p;)15 b(p)2335 1687 y Fr(1)2375 1673 y Fz(\))p Fs(R)2480 1640 y FA(0)2503 1673 y Fz(\()p Fs(p)2584 1687 y Fr(1)2624 1673 y Fs(;)g(p)2710 1687 y Fr(2)2749 1673 y Fz(\))2794 1649 y Fp(b)2784 1673 y Fs(\020)2831 1647 y FA(0)2854 1673 y Fz(\()p Fs(p)2935 1687 y Fr(2)2995 1673 y Fq(\000)20 b Fs(p)p Fz(\))p 1993 1714 1256 4 v 1993 1801 a(\()p Fs(E)5 b Fz(\()p Fs(p)p Fz(\))2216 1774 y Fr(2)2277 1801 y Fz(+)20 b Fs(\021)2416 1774 y Fr(2)2456 1801 y Fz(\))2491 1774 y Fr(1)p Fo(=)p Fr(4)2601 1801 y Fz(\()p Fs(E)5 b Fz(\()p Fs(p)2789 1815 y Fr(2)2830 1801 y Fz(\))2865 1774 y Fr(2)2925 1801 y Fz(+)19 b Fs(\021)3063 1774 y Fr(2)3103 1801 y Fz(\))3138 1774 y Fr(1)p Fo(=)p Fr(4)0 2036 y Fz(where)264 2012 y Fp(c)263 2036 y Fs(R)333 2010 y FA(0)356 2036 y Fz(\()p Fs(p;)c(q)s Fz(\))26 b(=)688 1991 y Fo(E)t Fr(\()p Fo(p)p FA(\000)p Fo(q)r Fr(\))p FA(j)955 1975 y Fb(b)943 1991 y Fo(R)p Fr(\()p Fo(p;q)r Fr(\))p FA(j)p 688 2015 472 4 v 758 2076 a Fo(E)t Fr(\()p Fo(p)p Fr(+)p Fo(q)r Fr(\))993 2056 y Fi(1)p Fg(=)p Fi(2)1199 2036 y Fz(and)1386 2012 y Fp(b)1376 2036 y Fs(\020)1423 2010 y FA(0)1446 2036 y Fz(\()p Fs(k)s Fz(\))g(=)f Fs(E)5 b Fz(\()p Fs(k)s Fz(\))1880 2003 y FA(\000)p Fr(1)1981 2012 y Fp(b)1976 2036 y Fs(\020)h Fz(\()p Fs(k)s Fz(\).)42 b(This)29 b(means)h(that)276 2333 y Fq(jh)p Fs(\032)383 2347 y Fr(2)p Fo(;)p Fr(0)478 2333 y Fs(;)15 b(\020)7 b Fq(ij)83 b(\024)899 2271 y Fz(4)p 872 2312 101 4 v 872 2395 a(2)p Fs(\031)998 2209 y Fp(Z)1088 2236 y Fr(+)p FA(1)1048 2415 y(\0001)1291 2271 y Fs(d\021)p 1243 2312 192 4 v 1243 2395 a(E)5 b Fz(\()p Fs(\021)s Fz(\))1460 2201 y Fp(\014)1460 2256 y(\014)1460 2310 y(\014)1460 2365 y(\014)1475 2201 y(\014)1475 2256 y(\014)1475 2310 y(\014)1475 2365 y(\014)1505 2333 y Fs(R)1575 2295 y FA(0)1598 2333 y Fs(R)1668 2295 y FA(0)1971 2271 y Fz(1)p 1701 2312 585 4 v 1701 2399 a(\()p Fq(j)p Fs(D)1836 2413 y Fr(0)1876 2399 y Fq(j)1901 2373 y Fr(2)1961 2399 y Fz(+)20 b Fs(\021)2100 2373 y Fr(2)2140 2399 y Fz(\))2175 2373 y Fr(1)p Fo(=)p Fr(4)2295 2333 y Fs(\020)2342 2295 y FA(0)2645 2271 y Fz(1)p 2375 2312 V 2375 2399 a(\()p Fq(j)p Fs(D)2510 2413 y Fr(0)2550 2399 y Fq(j)2575 2373 y Fr(2)2635 2399 y Fz(+)g Fs(\021)2774 2373 y Fr(2)2814 2399 y Fz(\))2849 2373 y Fr(1)p Fo(=)p Fr(4)2969 2201 y Fp(\014)2969 2256 y(\014)2969 2310 y(\014)2969 2365 y(\014)2985 2201 y(\014)2985 2256 y(\014)2985 2310 y(\014)2985 2365 y(\014)3015 2426 y Fd(S)3072 2435 y Fi(1)708 2615 y Fq(\024)973 2553 y Fz(4)p Fs(S)1074 2567 y Fr(6)p 872 2594 343 4 v 872 2677 a Fz(\(2)p Fs(\031)s Fz(\)\(4)p Fs(\031)s Fz(\))1239 2491 y Fp(Z)1330 2517 y Fr(+)p FA(1)1290 2697 y(\0001)1588 2553 y Fs(d\021)p 1485 2594 302 4 v 1485 2681 a(E)5 b Fz(\()p Fs(\021)s Fz(\))1675 2655 y Fr(3)p Fo(=)p Fr(2)1812 2538 y Fp(\014)1812 2592 y(\014)1827 2538 y(\014)1827 2592 y(\014)1857 2615 y Fs(R)1927 2577 y FA(0)1950 2538 y Fp(\014)1950 2592 y(\014)1965 2538 y(\014)1965 2592 y(\014)1996 2564 y Fr(2)1996 2651 y Fd(S)2053 2660 y Fi(2)2107 2538 y Fp(\014)2107 2592 y(\014)2122 2538 y(\014)2122 2592 y(\014)2152 2615 y Fs(\020)2199 2577 y FA(0)2222 2538 y Fp(\014)2222 2592 y(\014)2237 2538 y(\014)2237 2592 y(\014)2267 2651 y Fo(L)2315 2632 y Fi(6)2379 2615 y Fq(\024)2485 2544 y Fs(S)2541 2558 y Fr(6)2580 2544 y Fs(C)2645 2558 y Fr(6)2685 2544 y Fz(\()p Fs(C)2785 2558 y Fo(R)2843 2544 y Fz(\))2878 2511 y Fr(2)2918 2544 y Fs(K)2995 2563 y Fr(3)p Fo(=)p Fr(2)p 2485 2594 620 4 v 2767 2677 a Fs(\031)3115 2615 y Fq(j)-15 b(j)p Fs(Q)p Fq(j)g(j)3257 2577 y Fr(2)3257 2637 y FA(Q)3319 2615 y Fq(j)g(j)p Fs(\020)7 b Fq(j)-15 b(j)3436 2630 y FA(C)3477 2611 y Fl(0)0 2875 y Fz(b)m(y)30 b(\(46\),)i(sho)m(wing)f(that)1266 3047 y Fq(j)-15 b(j)p Fs(\032)1348 3061 y Fr(2)p Fo(;)p Fr(0)1443 3047 y Fq(j)g(j)1478 3061 y FA(C)1548 3047 y Fq(\024)1654 2985 y Fs(S)1710 2999 y Fr(6)1749 2985 y Fs(C)1814 2999 y Fr(6)1854 2985 y Fz(\()p Fs(C)1954 2999 y Fo(R)2012 2985 y Fz(\))2047 2952 y Fr(2)p 1654 3026 433 4 v 1843 3109 a Fs(\031)2097 3047 y(K)2174 3065 y Fr(3)p Fo(=)p Fr(2)2284 3047 y Fq(j)g(j)p Fs(Q)p Fq(j)g(j)2426 3009 y Fr(2)2426 3069 y FA(Q)2488 3047 y Fs(:)0 3343 y Fq(\017)56 b Fs(\032)148 3357 y Fr(1)p Fo(;)p Fr(1)242 3343 y Fz(.)40 b(Unfortunately)-8 b(,)29 b(as)f(for)g Fs(Q)1229 3357 y Fr(0)p Fo(;)p Fr(2)1323 3343 y Fz(,)g(w)m(e)h(ha)m(v)m(e)g(to)f(calculate)i Fs(\032)2246 3357 y Fr(1)p Fo(;)p Fr(1)2368 3343 y Fz(explicitely)-8 b(.)43 b(Let)28 b(us)f(start)h(for)g(instance)0 3456 y(with)i Fs(\032)254 3418 y Fr(+)p FA(\000\000)254 3482 y Fr(1)p Fo(;)p Fr(1)423 3456 y Fz(,)g(the)h(densit)m(y)g(asso)s (ciated)g(with)g(one)f(of)h(the)f(t)m(w)m(o)i(terms)e(of)h Fs(Q)2616 3470 y Fr(1)p Fo(;)p Fr(1)784 3749 y Fz(\(2)p Fs(\031)s Fz(\))954 3712 y FA(\000)p Fr(3)p Fo(=)p Fr(2)1136 3625 y Fp(Z)1186 3831 y Fj(R)1234 3813 y Fi(3)1288 3749 y Fs(dp)1381 3763 y Fr(1)1430 3688 y Fz(\003)1493 3655 y Fr(+)1553 3688 y Fz(\()p Fs(p)p Fz(\))1686 3665 y Fp(b)1669 3688 y Fs(R)q Fz(\()p Fs(p)20 b Fq(\000)g Fs(p)1977 3702 y Fr(1)2016 3688 y Fz(\)\003)2114 3655 y FA(\000)2174 3688 y Fz(\()p Fs(p)2255 3702 y Fr(1)2294 3688 y Fz(\))2346 3664 y Fp(b)2329 3688 y Fs(')2388 3661 y FA(0)2412 3688 y Fz(\()p Fs(p)2493 3702 y Fr(1)2553 3688 y Fq(\000)g Fs(q)s Fz(\)\003)2786 3655 y FA(\000)2845 3688 y Fz(\()p Fs(q)s Fz(\))p 1430 3728 1530 4 v 1617 3811 a(\()p Fs(E)5 b Fz(\()p Fs(p)p Fz(\))21 b(+)f Fs(E)5 b Fz(\()p Fs(q)s Fz(\)\)\()p Fs(E)g Fz(\()p Fs(p)p Fz(\))23 b(+)d Fs(E)5 b Fz(\()p Fs(p)2663 3825 y Fr(1)2703 3811 y Fz(\)\))2970 3749 y Fs(:)0 4013 y Fz(W)-8 b(e)32 b(use)e(the)g(same)h(metho)s(d)f (as)g(ab)s(o)m(v)m(e)i(and)e(estimate)i(for)e(some)h Fs(\020)h Fq(2)24 b(C)2516 3980 y FA(0)2560 4013 y Fq(\\)c Fs(L)2703 3980 y Fr(2)2772 4013 y Fz(the)31 b(term)346 4261 y Fp(c)335 4284 y Fs(Q)407 4299 y Fo(\020)447 4284 y Fz(\()p Fs(p;)15 b(p)p Fz(\))26 b(=)f(\(2)p Fs(\031)s Fz(\))941 4247 y FA(\000)p Fr(3)1052 4161 y Fp(Z)9 b(Z)1218 4284 y Fs(dp)1311 4298 y Fr(1)1366 4284 y Fs(dp)1459 4298 y Fr(2)1508 4223 y Fz(\003)1571 4190 y Fr(+)1630 4223 y Fz(\()p Fs(p)p Fz(\))1764 4200 y Fp(b)1746 4223 y Fs(R)r Fz(\()p Fs(p;)15 b(p)1984 4237 y Fr(1)2023 4223 y Fz(\)\003)2121 4190 y FA(\000)2181 4223 y Fz(\()p Fs(p)2262 4237 y Fr(1)2301 4223 y Fz(\))2353 4199 y Fp(b)2336 4223 y Fs(')2395 4197 y FA(0)2419 4223 y Fz(\()p Fs(p)2500 4237 y Fr(1)2560 4223 y Fq(\000)20 b Fs(p)2697 4237 y Fr(2)2736 4223 y Fz(\)\003)2834 4190 y FA(\000)2894 4223 y Fz(\()p Fs(p)2975 4237 y Fr(2)3014 4223 y Fz(\))p 1508 4264 1542 4 v 1680 4347 a(\()p Fs(E)5 b Fz(\()p Fs(p)p Fz(\))21 b(+)f Fs(E)5 b Fz(\()p Fs(p)2168 4361 y Fr(2)2208 4347 y Fz(\)\)\()p Fs(E)g Fz(\()p Fs(p)p Fz(\))22 b(+)e Fs(E)5 b Fz(\()p Fs(p)2767 4361 y Fr(1)2807 4347 y Fz(\)\))3065 4260 y Fp(b)3060 4284 y Fs(\020)h Fz(\()p Fs(p)3187 4298 y Fr(2)3247 4284 y Fq(\000)20 b Fs(p)p Fz(\))p Fs(;)0 4535 y Fz(b)m(y)512 4807 y Fq(j)547 4784 y Fp(c)537 4807 y Fs(Q)609 4822 y Fo(\020)649 4807 y Fz(\()p Fs(p;)15 b(p)p Fz(\))p Fq(j)84 b(\024)f Fz(\(2)p Fs(\031)s Fz(\))1284 4770 y FA(\000)p Fr(3)1394 4683 y Fp(Z)10 b(Z)1571 4746 y Fq(j)p Fz(\003)1659 4713 y Fr(+)1718 4746 y Fz(\()p Fs(p)p Fz(\))1852 4723 y Fp(b)1834 4746 y Fs(R)r Fz(\()p Fs(p;)15 b(p)2072 4760 y Fr(1)2111 4746 y Fz(\)\003)2209 4713 y FA(\000)2269 4746 y Fz(\()p Fs(p)2350 4760 y Fr(1)2389 4746 y Fz(\))p Fq(j)p 1571 4786 879 4 v 1763 4873 a Fs(E)5 b Fz(\()p Fs(p)21 b Fz(+)e Fs(p)2073 4887 y Fr(1)2113 4873 y Fz(\))2148 4847 y Fr(1)p Fo(=)p Fr(2)2565 4746 y Fq(j)2607 4722 y Fp(b)2590 4746 y Fs(')2649 4719 y FA(0)2673 4746 y Fz(\()p Fs(p)2754 4760 y Fr(1)2814 4746 y Fq(\000)h Fs(p)2951 4760 y Fr(2)2990 4746 y Fz(\))p Fq(j)p 2470 4786 677 4 v 2470 4873 a Fs(E)5 b Fz(\()p Fs(p)2623 4887 y Fr(1)2663 4873 y Fz(\))2698 4847 y Fr(1)p Fo(=)p Fr(2)2808 4873 y Fs(E)g Fz(\()p Fs(p)2961 4887 y Fr(2)3001 4873 y Fz(\))3036 4847 y Fr(1)p Fo(=)p Fr(3)3176 4807 y Fq(\002)1477 5080 y(\002)1558 5019 y(j)1589 4995 y Fp(b)1583 5019 y Fs(\020)i Fz(\()p Fs(p)1711 5033 y Fr(2)1770 5019 y Fq(\000)20 b Fs(p)p Fz(\))p Fq(j)h(\002)f(j)p Fz(\003)2167 4986 y FA(\000)2226 5019 y Fz(\()p Fs(p)2307 5033 y Fr(2)2347 5019 y Fz(\)\003)2445 4986 y Fr(+)2504 5019 y Fz(\()p Fs(p)p Fz(\))p Fq(j)p 1558 5060 1089 4 v 1854 5147 a Fs(E)5 b Fz(\()p Fs(p)21 b Fz(+)f Fs(p)2165 5161 y Fr(2)2204 5147 y Fz(\))2239 5120 y Fr(2)p Fo(=)p Fr(3)2656 5080 y Fs(dp)2749 5094 y Fr(1)2804 5080 y Fs(dp)2897 5094 y Fr(2)2936 5080 y Fs(;)960 5353 y Fq(\024)83 b Fz(2\(2)p Fs(\031)s Fz(\))1329 5315 y FA(\000)p Fr(3)p Fo(=)p Fr(2)1510 5229 y Fp(Z)10 b(Z)1687 5291 y Fs(E)5 b Fz(\()p Fs(p)21 b Fq(\000)f Fs(p)1998 5305 y Fr(1)2037 5291 y Fz(\))p Fq(j)p Fz(\003)2160 5258 y Fr(+)2219 5291 y Fz(\()p Fs(p)p Fz(\))2353 5268 y Fp(b)2335 5291 y Fs(R)r Fz(\()p Fs(p;)15 b(p)2573 5305 y Fr(1)2612 5291 y Fz(\)\003)2710 5258 y FA(\000)2770 5291 y Fz(\()p Fs(p)2851 5305 y Fr(1)2890 5291 y Fz(\))p Fq(j)p 1687 5332 1265 4 v 2071 5419 a Fs(E)5 b Fz(\()p Fs(p)21 b Fz(+)f Fs(p)2382 5433 y Fr(1)2421 5419 y Fz(\))2456 5393 y Fr(1)p Fo(=)p Fr(2)2981 5353 y Fq(\002)1295 5626 y(\002)1528 5541 y Fp(b)1511 5565 y Fs(f)9 b Fz(\()p Fs(p)1646 5579 y Fr(1)1706 5565 y Fq(\000)20 b Fs(p)1843 5579 y Fr(2)1882 5565 y Fz(\))p 1376 5605 677 4 v 1376 5692 a Fs(E)5 b Fz(\()p Fs(p)1529 5706 y Fr(1)1569 5692 y Fz(\))1604 5666 y Fr(1)p Fo(=)p Fr(2)1714 5692 y Fs(E)g Fz(\()p Fs(p)1867 5706 y Fr(2)1907 5692 y Fz(\))1942 5666 y Fr(1)p Fo(=)p Fr(3)2072 5603 y Fp(d)2063 5626 y Fs(M)2151 5641 y Fo(\020)2187 5622 y Fl(0)2213 5626 y Fz(\()p Fs(p)2294 5640 y Fr(2)2333 5626 y Fs(;)15 b(p)p Fz(\))p Fs(dp)2547 5640 y Fr(1)2602 5626 y Fs(dp)2695 5640 y Fr(2)2735 5626 y Fs(;)1844 5906 y Fz(27)p eop end %%Page: 28 28 TeXDict begin 28 27 bop 0 90 a Fz(with)224 66 y Fp(b)207 90 y Fs(f)9 b Fz(\()p Fs(k)s Fz(\))27 b(:=)e Fs(E)5 b Fz(\()p Fs(k)s Fz(\))p Fq(j)763 66 y Fp(b)746 90 y Fs(')805 63 y FA(0)830 90 y Fz(\()p Fs(k)s Fz(\))p Fq(j)31 b Fz(and)1193 66 y Fp(b)1183 90 y Fs(\020)1230 63 y FA(0)1253 90 y Fz(\()p Fs(k)s Fz(\))26 b(:=)f Fq(j)1551 66 y Fp(b)1545 90 y Fs(\020)7 b Fz(\()p Fs(k)s Fz(\))p Fq(j)p Fs(=E)e Fz(\()p Fs(k)s Fz(\).)44 b(No)m(w)498 334 y Fq(j)533 311 y Fp(c)523 334 y Fs(Q)595 349 y Fo(\020)635 334 y Fz(\()p Fs(p;)15 b(p)p Fz(\))p Fq(j)26 b(\024)f Fz(2\(2)p Fs(\031)s Fz(\))1199 296 y FA(\000)p Fr(3)p Fo(=)p Fr(2)1381 210 y Fp(Z)9 b(Z)1556 311 y(c)1547 334 y Fs(R)1616 348 y Fr(1)1656 334 y Fz(\()p Fs(p;)15 b(p)1823 348 y Fr(1)1862 334 y Fz(\))2060 248 y Fp(b)2043 272 y Fs(f)9 b Fz(\()p Fs(p)2178 286 y Fr(1)2238 272 y Fq(\000)20 b Fs(p)2375 286 y Fr(2)2414 272 y Fz(\))p 1907 313 677 4 v 1907 400 a Fs(E)5 b Fz(\()p Fs(p)2060 414 y Fr(1)2101 400 y Fz(\))2136 374 y Fr(1)p Fo(=)p Fr(2)2246 400 y Fs(E)g Fz(\()p Fs(p)2399 414 y Fr(2)2439 400 y Fz(\))2474 374 y Fr(1)p Fo(=)p Fr(3)2604 311 y Fp(d)2594 334 y Fs(M)2682 349 y Fo(\020)2718 330 y Fl(0)2744 334 y Fz(\()p Fs(p)2825 348 y Fr(2)2865 334 y Fs(;)15 b(p)p Fz(\))g Fs(dp)3094 348 y Fr(1)3149 334 y Fs(dp)3242 348 y Fr(2)0 556 y Fz(with)995 692 y Fp(c)987 715 y Fs(R)1056 729 y Fr(1)1095 715 y Fz(\()p Fs(p;)g(p)1262 729 y Fr(1)1302 715 y Fz(\))25 b(:=)1494 653 y Fs(E)5 b Fz(\()p Fs(p)20 b Fq(\000)g Fs(p)1804 667 y Fr(1)1843 653 y Fz(\))p Fq(j)p Fz(\003)1966 620 y Fr(+)2026 653 y Fz(\()p Fs(p)p Fz(\))2160 630 y Fp(b)2142 653 y Fs(R)q Fz(\()p Fs(p;)15 b(p)2379 667 y Fr(1)2419 653 y Fz(\)\003)2517 620 y FA(\000)2576 653 y Fz(\()p Fs(p)2657 667 y Fr(1)2697 653 y Fz(\))p Fq(j)p 1494 694 1265 4 v 1878 781 a Fs(E)5 b Fz(\()p Fs(p)21 b Fz(+)f Fs(p)2189 795 y Fr(1)2228 781 y Fz(\))2263 755 y Fr(1)p Fo(=)p Fr(2)2768 715 y Fs(:)0 914 y Fz(W)-8 b(e)32 b(th)m(us)e(ha)m(v)m (e)690 1117 y Fq(jh)p Fs(\032)797 1078 y Fr(+)p FA(\000\000)797 1143 y Fr(1)p Fo(;)p Fr(1)966 1117 y Fs(;)15 b(\020)7 b Fq(i)q(j)83 b(\024)g Fz(2)1411 985 y Fp(\014)1411 1039 y(\014)1411 1094 y(\014)1411 1148 y(\014)1426 985 y(\014)1426 1039 y(\014)1426 1094 y(\014)1426 1148 y(\014)1457 1117 y Fs(R)1526 1131 y Fr(1)1690 1055 y Fz(1)p 1575 1096 276 4 v 1575 1183 a Fq(j)p Fs(D)1675 1197 y Fr(0)1715 1183 y Fq(j)1740 1156 y Fr(1)p Fo(=)p Fr(2)1860 1117 y Fs(f)2039 1055 y Fz(1)p 1925 1096 V 1925 1183 a Fq(j)p Fs(D)2025 1197 y Fr(0)2064 1183 y Fq(j)2089 1156 y Fr(1)p Fo(=)p Fr(3)2210 1117 y Fs(M)2298 1132 y Fo(\020)2334 1113 y Fl(0)2360 985 y Fp(\014)2360 1039 y(\014)2360 1094 y(\014)2360 1148 y(\014)2375 985 y(\014)2375 1039 y(\014)2375 1094 y(\014)2375 1148 y(\014)2405 1210 y Fd(S)2462 1191 y Fi(1)1197 1375 y Fq(\024)g Fz(2)p Fq(j)-15 b(j)p Fz(\003)1494 1337 y Fr(+)1554 1375 y Fs(R)q Fz(\003)1687 1337 y FA(\000)1746 1375 y Fq(j)g(j)1781 1389 y FA(R)1860 1297 y Fp(\014)1860 1352 y(\014)1876 1297 y(\014)1876 1352 y(\014)1906 1375 y Fs(M)1994 1390 y Fo(\020)2030 1371 y Fl(0)2056 1297 y Fp(\014)2056 1352 y(\014)2071 1297 y(\014)2071 1352 y(\014)2102 1411 y Fd(S)2159 1420 y Fi(2)2213 1243 y Fp(\014)2213 1297 y(\014)2213 1352 y(\014)2213 1407 y(\014)2228 1243 y(\014)2228 1297 y(\014)2228 1352 y(\014)2228 1407 y(\014)2383 1313 y Fz(1)p 2268 1354 V 2268 1441 a Fq(j)p Fs(D)2368 1455 y Fr(0)2408 1441 y Fq(j)2433 1415 y Fr(1)p Fo(=)p Fr(2)2553 1375 y Fs(f)2732 1313 y Fz(1)p 2617 1354 V 2617 1441 a Fq(j)p Fs(D)2717 1455 y Fr(0)2757 1441 y Fq(j)2782 1415 y Fr(1)p Fo(=)p Fr(3)2903 1243 y Fp(\014)2903 1297 y(\014)2903 1352 y(\014)2903 1407 y(\014)2918 1243 y(\014)2918 1297 y(\014)2918 1352 y(\014)2918 1407 y(\014)2948 1468 y Fd(S)3005 1476 y Fl(1)1197 1641 y Fq(\024)83 b Fz(2)p Fq(j)-15 b(j)p Fz(\003)1494 1604 y Fr(+)1554 1641 y Fs(R)q Fz(\003)1687 1604 y FA(\000)1746 1641 y Fq(j)g(j)1781 1655 y FA(R)1860 1564 y Fp(\014)1860 1618 y(\014)1876 1564 y(\014)1876 1618 y(\014)1906 1641 y Fs(M)1994 1656 y Fo(\020)2030 1638 y Fl(0)2056 1564 y Fp(\014)2056 1618 y(\014)2071 1564 y(\014)2071 1618 y(\014)2102 1677 y Fd(S)2159 1686 y Fi(2)2213 1509 y Fp(\014)2213 1564 y(\014)2213 1618 y(\014)2213 1673 y(\014)2228 1509 y(\014)2228 1564 y(\014)2228 1618 y(\014)2228 1673 y(\014)2383 1580 y Fz(1)p 2268 1620 V 2268 1707 a Fq(j)p Fs(D)2368 1721 y Fr(0)2408 1707 y Fq(j)2433 1681 y Fr(1)p Fo(=)p Fr(2)2553 1641 y Fs(f)2732 1580 y Fz(1)p 2617 1620 V 2617 1707 a Fq(j)p Fs(D)2717 1721 y Fr(0)2757 1707 y Fq(j)2782 1681 y Fr(1)p Fo(=)p Fr(3)2903 1509 y Fp(\014)2903 1564 y(\014)2903 1618 y(\014)2903 1673 y(\014)2918 1509 y(\014)2918 1564 y(\014)2918 1618 y(\014)2918 1673 y(\014)2948 1734 y Fd(S)3005 1743 y Fi(6)1197 1901 y Fq(\024)1361 1839 y Fs(S)1417 1853 y Fr(6)p Fo(;)p Fr(5)1511 1839 y Fs(C)1576 1853 y Fo(M)1655 1839 y Fs(C)1720 1853 y Fr(6)p 1361 1880 399 4 v 1510 1963 a Fz(2)p Fs(\031)1769 1901 y Fq(j)g(j)p Fz(\003)1867 1863 y Fr(+)1927 1901 y Fs(R)q Fz(\003)2060 1863 y FA(\000)2118 1901 y Fq(j)g(j)2153 1915 y FA(R)2218 1901 y Fq(j)g(j)p Fs(\020)7 b Fq(j)-15 b(j)2335 1916 y FA(C)2376 1897 y Fl(0)2403 1901 y Fq(j)g(j)p Fs(\032)2485 1863 y FA(0)2508 1901 y Fq(j)g(j)2543 1915 y FA(C)2589 1901 y Fs(;)0 2097 y Fz(and)30 b(\014nally)1124 2247 y Fq(j)-15 b(j)p Fs(\032)1206 2209 y Fr(+)p FA(\000\000)1206 2273 y Fr(1)p Fo(;)p Fr(1)1375 2247 y Fq(j)g(j)1410 2261 y FA(C)1481 2247 y Fq(\024)1587 2185 y Fs(S)1643 2199 y Fr(6)p Fo(;)p Fr(5)1737 2185 y Fs(C)1802 2199 y Fo(M)1881 2185 y Fs(C)1946 2199 y Fr(6)p 1587 2226 V 1736 2309 a Fz(2)p Fs(\031)1995 2247 y Fq(j)g(j)p Fz(\003)2093 2209 y Fr(+)2153 2247 y Fs(R)q Fz(\003)2286 2209 y FA(\000)2345 2247 y Fq(j)g(j)2380 2261 y FA(R)2444 2247 y Fq(j)g(j)p Fs(\032)2526 2209 y FA(0)2550 2247 y Fq(j)g(j)2585 2261 y FA(C)2630 2247 y Fs(:)141 2435 y Fz(W)-8 b(e)32 b(no)m(w)e(treat)i Fs(\032)757 2397 y Fr(+)p FA(\000)p Fr(+)757 2461 y(1)p Fo(;)p Fr(1)956 2435 y Fz(and)d(estimate)346 2673 y Fp(c)335 2696 y Fs(Q)407 2711 y Fo(\020)447 2696 y Fz(\()p Fs(p;)15 b(p)p Fz(\))26 b(=)f(\(2)p Fs(\031)s Fz(\))941 2658 y FA(\000)p Fr(3)1052 2572 y Fp(Z)9 b(Z)1218 2696 y Fs(dp)1311 2710 y Fr(1)1366 2696 y Fs(dp)1459 2710 y Fr(2)1508 2634 y Fz(\003)1571 2601 y Fr(+)1630 2634 y Fz(\()p Fs(p)p Fz(\))1764 2611 y Fp(b)1746 2634 y Fs(R)r Fz(\()p Fs(p;)15 b(p)1984 2648 y Fr(1)2023 2634 y Fz(\)\003)2121 2601 y FA(\000)2181 2634 y Fz(\()p Fs(p)2262 2648 y Fr(1)2301 2634 y Fz(\))2353 2610 y Fp(b)2336 2634 y Fs(')2395 2608 y FA(0)2419 2634 y Fz(\()p Fs(p)2500 2648 y Fr(1)2560 2634 y Fq(\000)20 b Fs(p)2697 2648 y Fr(2)2736 2634 y Fz(\)\003)2834 2601 y Fr(+)2894 2634 y Fz(\()p Fs(p)2975 2648 y Fr(2)3014 2634 y Fz(\))p 1508 2675 1542 4 v 1660 2758 a(\()p Fs(E)5 b Fz(\()p Fs(p)p Fz(\))22 b(+)e Fs(E)5 b Fz(\()p Fs(p)2149 2772 y Fr(1)2189 2758 y Fz(\)\)\()p Fs(E)g Fz(\()p Fs(p)2447 2772 y Fr(1)2488 2758 y Fz(\))20 b(+)g Fs(E)5 b Fz(\()p Fs(p)2787 2772 y Fr(2)2827 2758 y Fz(\)\))3065 2672 y Fp(b)3060 2696 y Fs(\020)h Fz(\()p Fs(p)3187 2710 y Fr(2)3247 2696 y Fq(\000)20 b Fs(p)p Fz(\))p Fs(;)0 2914 y Fz(b)m(y)83 3177 y Fq(j)118 3154 y Fp(c)108 3177 y Fs(Q)180 3192 y Fo(\020)220 3177 y Fz(\()p Fs(p;)15 b(p)p Fz(\))p Fq(j)26 b(\024)f Fz(2\(2)p Fs(\031)s Fz(\))784 3140 y FA(\000)p Fr(3)895 3054 y Fp(Z)10 b(Z)1072 3116 y Fs(E)5 b Fz(\()p Fs(p)20 b Fq(\000)g Fs(p)1382 3130 y Fr(1)1421 3116 y Fz(\))p Fq(j)p Fz(\003)1544 3083 y Fr(+)1604 3116 y Fz(\()p Fs(p)p Fz(\))1738 3093 y Fp(b)1720 3116 y Fs(R)q Fz(\()p Fs(p;)15 b(p)1957 3130 y Fr(1)1997 3116 y Fz(\)\003)2095 3083 y FA(\000)2155 3116 y Fz(\()p Fs(p)2236 3130 y Fr(1)2275 3116 y Fz(\))p Fq(j)p 1072 3156 1265 4 v 1456 3243 a Fs(E)5 b Fz(\()p Fs(p)21 b Fz(+)f Fs(p)1767 3257 y Fr(1)1806 3243 y Fz(\))1841 3217 y Fr(1)p Fo(=)p Fr(2)2346 3177 y Fq(\002)1865 3451 y(\002)1983 3365 y Fp(b)1966 3389 y Fs(f)9 b Fz(\()p Fs(p)2101 3403 y Fr(1)2161 3389 y Fq(\000)20 b Fs(p)2298 3403 y Fr(2)2337 3389 y Fz(\))p Fq(j)p Fz(\003)2460 3356 y FA(\000)2520 3389 y Fz(\()p Fs(p)2601 3403 y Fr(1)2640 3389 y Fz(\)\003)2738 3356 y Fr(+)2798 3389 y Fz(\()p Fs(p)2879 3403 y Fr(2)2918 3389 y Fz(\))p Fq(j)p 1966 3430 1014 4 v 2205 3517 a Fs(E)5 b Fz(\()p Fs(p)2358 3531 y Fr(1)2418 3517 y Fz(+)20 b Fs(p)2555 3531 y Fr(2)2594 3517 y Fz(\))2629 3490 y Fr(2)p Fo(=)p Fr(3)3008 3365 y Fp(b)2999 3389 y Fs(\020)3046 3363 y FA(0)3068 3389 y Fz(\()p Fs(p)3149 3403 y Fr(2)3209 3389 y Fq(\000)g Fs(p)p Fz(\))p 2999 3430 383 4 v 3021 3517 a Fs(E)5 b Fz(\()p Fs(p)3174 3531 y Fr(2)3214 3517 y Fz(\))3249 3490 y Fr(5)p Fo(=)p Fr(6)3391 3451 y Fs(dp)3484 3465 y Fr(1)3539 3451 y Fs(dp)3632 3465 y Fr(2)3671 3451 y Fs(:)0 3673 y Fz(Using)31 b(the)f(same)h(argumen)m(t)g(as)f(ab)s(o)m(v) m(e,)i(w)m(e)f(arriv)m(e)g(at)1124 3885 y Fq(j)-15 b(j)p Fs(\032)1206 3847 y Fr(+)p FA(\000)p Fr(+)1206 3911 y(1)p Fo(;)p Fr(1)1375 3885 y Fq(j)g(j)1410 3899 y FA(C)1481 3885 y Fq(\024)1587 3823 y Fs(S)1643 3837 y Fr(6)p Fo(;)p Fr(5)1737 3823 y Fs(C)1802 3837 y Fo(M)1881 3823 y Fs(C)1946 3837 y Fr(6)p 1587 3864 399 4 v 1736 3948 a Fz(2)p Fs(\031)1995 3885 y Fq(j)g(j)p Fz(\003)2093 3848 y Fr(+)2153 3885 y Fs(R)q Fz(\003)2286 3848 y FA(\000)2345 3885 y Fq(j)g(j)2380 3899 y FA(R)2444 3885 y Fq(j)g(j)p Fs(\032)2526 3848 y FA(0)2550 3885 y Fq(j)g(j)2585 3899 y FA(C)2630 3885 y Fs(:)0 4096 y Fz(T)-8 b(o)31 b(treat)g Fs(\032)403 4058 y Fr(++)p FA(\000)403 4122 y Fr(1)p Fo(;)p Fr(1)572 4096 y Fz(,)g(w)m(e)g(remark)f(that)689 4289 y(1)p 93 4330 1238 4 v 93 4413 a(\()p Fs(E)5 b Fz(\()p Fs(p)p Fz(\))21 b(+)f Fs(E)5 b Fz(\()p Fs(p)581 4427 y Fr(2)621 4413 y Fz(\)\)\()p Fs(E)g Fz(\()p Fs(p)879 4427 y Fr(1)920 4413 y Fz(\))21 b(+)f Fs(E)5 b Fz(\()p Fs(p)1220 4427 y Fr(2)1259 4413 y Fz(\)\))1365 4351 y Fq(\024)2067 4289 y Fz(1)p 1471 4330 V 1471 4413 a(\()p Fs(E)g Fz(\()p Fs(p)p Fz(\))22 b(+)e Fs(E)5 b Fz(\()p Fs(p)1960 4427 y Fr(1)1999 4413 y Fz(\)\)\()p Fs(E)g Fz(\()p Fs(p)2257 4427 y Fr(1)2298 4413 y Fz(\))21 b(+)f Fs(E)5 b Fz(\()p Fs(p)2598 4427 y Fr(2)2638 4413 y Fz(\)\))2388 4589 y(+)3065 4527 y(1)p 2489 4568 1198 4 v 2489 4651 a(\()p Fs(E)g Fz(\()p Fs(p)p Fz(\))21 b(+)f Fs(E)5 b Fz(\()p Fs(p)2977 4665 y Fr(1)3017 4651 y Fz(\)\)\()p Fs(E)g Fz(\()p Fs(p)p Fz(\))22 b(+)e Fs(E)5 b Fz(\()p Fs(p)3576 4665 y Fr(2)3616 4651 y Fz(\)\))0 4807 y(and)30 b(use)g(the)g(same)h(estimates)h(as)f (ab)s(o)m(v)m(e)g(to)g(get)1124 5020 y Fq(j)-15 b(j)p Fs(\032)1206 4981 y Fr(++)p FA(\000)1206 5046 y Fr(1)p Fo(;)p Fr(1)1375 5020 y Fq(j)g(j)1410 5034 y FA(C)1481 5020 y Fq(\024)1587 4958 y Fs(S)1643 4972 y Fr(6)p Fo(;)p Fr(5)1737 4958 y Fs(C)1802 4972 y Fo(M)1881 4958 y Fs(C)1946 4972 y Fr(6)p 1587 4999 399 4 v 1758 5082 a Fs(\031)1995 5020 y Fq(j)g(j)p Fz(\003)2093 4982 y Fr(+)2153 5020 y Fs(R)q Fz(\003)2286 4982 y FA(\000)2345 5020 y Fq(j)g(j)2380 5034 y FA(R)2444 5020 y Fq(j)g(j)p Fs(\032)2526 4982 y FA(0)2550 5020 y Fq(j)g(j)2585 5034 y FA(C)2630 5020 y Fs(:)0 5228 y Fz(Finally)-8 b(,)32 b(since)550 5160 y Fp(P)646 5255 y Fo(\017)675 5264 y Fi(1)709 5255 y Fo(;\017)758 5264 y Fi(2)792 5255 y FA(2f\006g)983 5228 y Fq(j)-15 b(j)p Fz(\003)1081 5195 y Fo(\017)1110 5204 y Fi(1)1149 5228 y Fs(R)q Fz(\003)1282 5195 y Fo(\017)1311 5204 y Fi(2)1349 5228 y Fq(j)g(j)1384 5195 y Fr(2)1384 5255 y FA(R)1474 5228 y Fz(=)25 b Fq(j)-15 b(j)p Fs(R)q Fq(j)g(j)1710 5195 y Fr(2)1710 5255 y FA(R)1775 5228 y Fz(,)31 b(w)m(e)f(end)g(up)f(with)327 5528 y Fq(j)-15 b(j)p Fs(\032)409 5542 y Fr(1)p Fo(;)p Fr(1)504 5528 y Fq(j)g(j)539 5542 y FA(C)610 5528 y Fq(\024)25 b Fz(2)761 5466 y Fs(S)817 5480 y Fr(6)p Fo(;)p Fr(5)911 5466 y Fs(C)976 5480 y Fo(M)1055 5466 y Fs(C)1120 5480 y Fr(6)p 761 5507 V 933 5591 a Fs(\031)1169 5528 y Fq(j)-15 b(j)p Fs(\032)1251 5491 y FA(0)1275 5528 y Fq(j)g(j)1310 5542 y FA(C)1371 5346 y Fp(0)1371 5509 y(@)1544 5442 y(X)1450 5643 y Fo(\017)1479 5652 y Fi(1)1513 5643 y Fo(;\017)1562 5652 y Fi(2)1596 5643 y FA(2f\006g)1784 5528 y Fq(j)g(j)p Fz(\003)1882 5491 y Fo(\017)1911 5500 y Fi(1)1949 5528 y Fs(R)q Fz(\003)2082 5491 y Fo(\017)2111 5500 y Fi(2)2150 5528 y Fq(j)g(j)2185 5542 y FA(R)2249 5346 y Fp(1)2249 5509 y(A)2354 5528 y Fq(\024)25 b Fz(4)2505 5466 y Fs(S)2561 5480 y Fr(6)p Fo(;)p Fr(5)2656 5466 y Fs(C)2721 5480 y Fo(M)2800 5466 y Fs(C)2865 5480 y Fr(6)2904 5466 y Fs(C)2969 5480 y Fo(R)p 2505 5507 522 4 v 2739 5591 a Fs(\031)3037 5528 y Fq(j)-15 b(j)p Fs(\032)3119 5491 y FA(0)3142 5528 y Fq(j)g(j)3177 5542 y FA(C)3223 5528 y Fq(j)g(j)p Fs(Q)p Fq(j)g(j)3365 5542 y FA(Q)3427 5528 y Fs(:)1844 5906 y Fz(28)p eop end %%Page: 29 29 TeXDict begin 29 28 bop 0 79 a Fe(4.3.3)105 b(The)35 b(general)g Fs(n)952 46 y Fo(th)1057 79 y Fe(order)g(case)0 251 y Fz(No)m(w)24 b(that)g(w)m(e)f(ha)m(v)m(e)i(explained)e(ho)m(w)g (the)h(pro)s(of)e(w)m(orks)h(for)g(the)h(second)f(order,)h(let)h(us)d (estimate)j(the)e(general)0 364 y Fs(n)55 331 y Fo(th)155 364 y Fz(order)30 b(term.)0 514 y Fe(Lemma)35 b(13.)42 b Fy(We)32 b(have)h(the)g(fol)5 b(lowing)34 b(estimates)509 736 y Fq(8)p Fs(n)24 b Fq(\025)h Fz(3)p Fs(;)202 b Fq(j)-15 b(j)p Fs(Q)1114 750 y Fo(n)1161 736 y Fq(j)g(j)1196 750 y FA(Q)1284 736 y Fq(\024)24 b Fs(nK)1521 726 y Fg(n)p 1521 738 39 3 v 1525 779 a Fi(2)1574 736 y Fs(C)1639 750 y Fo(Q)1713 658 y Fp(\014)1713 713 y(\014)1729 658 y(\014)1729 713 y(\014)1759 736 y Fz(\()p Fs(Q;)15 b(\032)1953 698 y FA(0)1977 736 y Fz(\))2012 658 y Fp(\014)2012 713 y(\014)2027 658 y(\014)2027 713 y(\014)2058 685 y Fo(n)2120 736 y Fs(;)80 b Fy(with)66 b Fs(C)2520 750 y Fo(Q)2605 736 y Fz(=)2701 656 y Fq(p)p 2777 656 46 4 v 80 x Fz(2)2837 608 y Fp(\022)2914 674 y Fs(S)2970 688 y Fr(6)3009 674 y Fs(C)3074 688 y Fr(6)p 2914 715 200 4 v 2926 799 a Fz(2)2971 733 y Fq(p)p 3047 733 56 4 v 66 x Fs(\031)3124 608 y Fp(\023)3191 630 y Fr(3)3245 736 y Fs(;)461 1026 y Fq(8)p Fs(n)25 b Fq(\025)g Fz(5)p Fs(;)201 b Fq(j)-15 b(j)p Fs(\032)1041 1040 y Fo(n)1089 1026 y Fq(j)g(j)1124 1040 y FA(C)1194 1026 y Fq(\024)25 b Fs(nK)1432 1027 y Fg(n)p Fi(+1)p 1432 1040 116 3 v 1475 1081 a(2)1562 1026 y Fs(C)1627 1040 y Fo(\032)1682 949 y Fp(\014)1682 1003 y(\014)1697 949 y(\014)1697 1003 y(\014)1727 1026 y Fz(\()p Fs(Q;)15 b(\032)1921 988 y FA(0)1945 1026 y Fz(\))1980 949 y Fp(\014)1980 1003 y(\014)1996 949 y(\014)1996 1003 y(\014)2026 975 y Fo(n)2088 1026 y Fs(;)81 b Fy(with)66 b Fs(C)2489 1040 y Fo(\032)2554 1026 y Fz(=)2660 964 y Fs(S)2716 978 y Fr(6)2755 964 y Fs(C)2820 978 y Fr(6)p 2660 1005 200 4 v 2710 1088 a Fz(4)p Fs(\031)2885 898 y Fp(\022)2962 964 y Fs(S)3018 978 y Fr(6)3057 964 y Fs(C)3122 978 y Fr(6)p 2962 1005 V 2973 1089 a Fz(2)3018 1023 y Fq(p)p 3095 1023 56 4 v 3095 1089 a Fs(\031)3171 898 y Fp(\023)3238 920 y Fr(5)3293 1026 y Fs(;)748 1301 y Fq(j)-15 b(j)p Fs(\032)830 1315 y Fr(4)870 1301 y Fq(j)g(j)905 1315 y FA(C)975 1301 y Fq(\024)25 b Fs(C)1136 1315 y Fo(\032)1172 1324 y Fi(4)1226 1223 y Fp(\014)1226 1278 y(\014)1242 1223 y(\014)1242 1278 y(\014)1272 1301 y Fz(\()p Fs(Q;)15 b(\032)1466 1263 y FA(0)1490 1301 y Fz(\))1525 1223 y Fp(\014)1525 1278 y(\014)1540 1223 y(\014)1540 1278 y(\014)1571 1250 y Fr(4)1625 1301 y Fs(;)81 b Fy(with)66 b Fs(C)2026 1315 y Fo(\032)2062 1324 y Fi(4)2126 1301 y Fz(:=)2257 1239 y Fs(K)2334 1253 y Fr(2)2374 1239 y Fs(S)2430 1253 y Fr(6)2469 1239 y Fs(C)2534 1253 y Fr(6)p 2257 1280 317 4 v 2388 1363 a Fs(\031)2598 1172 y Fp(\022)2675 1239 y Fs(S)2731 1253 y Fr(6)2770 1239 y Fs(C)2835 1253 y Fr(6)p 2675 1280 200 4 v 2687 1363 a Fz(2)2732 1298 y Fq(p)p 2808 1298 56 4 v 65 x Fs(\031)2885 1172 y Fp(\023)2952 1195 y Fr(2)3006 1301 y Fs(:)0 1490 y Fy(Ther)-5 b(efor)g(e,)1130 1603 y Fq(8)p Fs(n)24 b Fq(\025)h Fz(4)p Fs(;)202 b Fq(j)-15 b(j)p Fz(\()p Fs(Q)1770 1617 y Fo(n)1818 1603 y Fs(;)15 b(\032)1905 1617 y Fo(n)1952 1603 y Fz(\))p Fq(j)-15 b(j)26 b(\024)f Fs(\024)2196 1617 y Fo(n)2258 1526 y Fp(\014)2258 1580 y(\014)2274 1526 y(\014)2274 1580 y(\014)2304 1603 y Fz(\()p Fs(Q;)15 b(\032)2498 1566 y FA(0)2522 1603 y Fz(\))2557 1526 y Fp(\014)2557 1580 y(\014)2572 1526 y(\014)2572 1580 y(\014)2603 1552 y Fo(n)0 1748 y Fy(with)455 1861 y Fs(\024)507 1875 y Fr(4)572 1861 y Fz(=)25 b(4)p Fs(C)778 1875 y Fo(R)836 1861 y Fs(K)913 1875 y Fr(2)953 1861 y Fs(C)1018 1875 y Fo(Q)1077 1781 y Fq(p)p 1153 1781 46 4 v 80 x Fz(2)c(+)f(2)1355 1791 y Fq(p)p 1431 1791 56 4 v 70 x Fs(\031)s(C)1551 1875 y Fo(\032)1587 1884 y Fi(4)1626 1861 y Fs(;)201 b(\024)1904 1875 y Fo(n)1977 1861 y Fz(=)25 b Fs(nC)2193 1875 y Fo(R)2250 1861 y Fs(K)2337 1851 y Fg(n)p 2337 1863 39 3 v 2341 1904 a Fi(2)2390 1861 y Fs(C)2455 1875 y Fo(Q)2514 1781 y Fq(p)p 2590 1781 46 4 v 80 x Fz(2)c(+)f(2)p Fs(nK)2934 1862 y Fg(n)p Fi(+1)p 2934 1875 116 3 v 2976 1916 a(2)3063 1861 y Fs(C)3128 1875 y Fo(\032)3168 1791 y Fq(p)p 3244 1791 56 4 v 70 x Fs(\031)s(:)141 2043 y Fz(Remark)29 b(that)h(it)f(can)h(b)s(e)e(pro)m(v)m(ed)h(that)h Fs(K)1622 2057 y Fo(n)1694 2043 y Fq(\030)1765 2057 y Fo(n)p FA(!1)2012 2007 y Fo(C)p 1988 2022 102 4 v 1988 2032 a FA(p)p 2047 2032 43 3 v 48 x Fo(n)2100 2043 y Fz(,)g(whic)m(h)e(giv)m(es)j(the)e (claimed)h(b)s(eha)m(viour)e(for)h Fs(\024)3732 2057 y Fo(n)0 2156 y Fz(as)i Fs(n)24 b Fq(!)i(1)p Fz(.)0 2304 y Fy(Pr)-5 b(o)g(of)34 b({)63 b Fe(Step)35 b(1)g(:)47 b(Estimates)34 b(on)h(the)f(exc)m(hange)i(term)f Fs(Q)2339 2318 y Fo(n)2386 2304 y Fe(.)0 2417 y Fq(\017)61 b Fs(Q)178 2432 y Fo(k)r(;l)295 2417 y Fy(with)33 b Fs(k)28 b Fq(\025)d Fz(1)33 b Fy(and)h Fs(k)23 b Fz(+)d Fs(l)27 b Fz(=)e Fs(n)g Fq(\025)g Fz(3.)41 b(Recall)32 b(that)435 2651 y Fs(Q)507 2666 y Fo(k)r(;l)617 2651 y Fz(=)723 2590 y(\()p Fq(\000)p Fz(1\))909 2557 y Fo(l)q Fr(+1)p 723 2630 304 4 v 824 2714 a Fz(2)p Fs(\031)1414 2565 y Fp(X)1051 2766 y Fo(I)5 b FA([)p Fo(J)h Fr(=)p FA(f)p Fr(1)p Fo(;:::;n)p FA(g)p Fo(;)28 b FA(j)p Fo(I)5 b FA(j)p Fr(=)p Fo(k)r(;)28 b FA(j)p Fo(J)6 b FA(j)p Fr(=)p Fo(l)1924 2527 y Fp(Z)2015 2554 y Fr(+)p FA(1)1975 2734 y(\0001)2160 2651 y Fs(d\021)2397 2590 y Fz(1)p 2265 2630 309 4 v 2265 2714 a Fs(D)2343 2687 y Fr(0)2403 2714 y Fz(+)20 b Fs(i\021)2638 2538 y Fo(n)2602 2565 y Fp(Y)2599 2760 y Fo(j)t Fr(=1)2736 2523 y Fp(\022)2803 2651 y Fs(R)2872 2665 y Fo(j)3050 2590 y Fz(1)p 2919 2630 V 2919 2714 a Fs(D)2997 2687 y Fr(0)3056 2714 y Fz(+)g Fs(i\021)3237 2523 y Fp(\023)3319 2651 y Fs(;)0 2917 y Fz(where)30 b Fs(R)332 2931 y Fo(j)394 2917 y Fz(=)25 b Fs(R)31 b Fz(if)f Fs(j)h Fq(2)25 b Fs(I)37 b Fz(and)30 b Fs(R)1150 2931 y Fo(j)1212 2917 y Fz(=)25 b Fs(')1367 2884 y FA(0)1421 2917 y Fz(if)30 b Fs(j)h Fq(2)25 b Fs(J)9 b Fz(.)41 b(F)-8 b(or)31 b(the)f(sak)m(e)i(of)e (simplicit)m(y)-8 b(,)33 b(w)m(e)e(treat)g(only)746 3151 y Fs(Q)818 3113 y FA(0)818 3174 y Fo(k)r(;l)927 3151 y Fz(=)1061 3089 y(1)p 1033 3130 101 4 v 1033 3213 a(2)p Fs(\031)1159 3027 y Fp(Z)1250 3053 y Fr(+)p FA(1)1209 3233 y(\0001)1394 3151 y Fs(d\021)1631 3089 y Fz(1)p 1499 3130 309 4 v 1499 3213 a Fs(D)1577 3187 y Fr(0)1638 3213 y Fz(+)19 b Fs(i\021)1833 3023 y Fp(\022)1900 3151 y Fs(R)2111 3089 y Fz(1)p 1980 3130 V 1980 3213 a Fs(D)2058 3187 y Fr(0)2117 3213 y Fz(+)h Fs(i\021)2298 3023 y Fp(\023)2365 3045 y Fo(k)2423 3023 y Fp(\022)2490 3151 y Fs(')2549 3113 y FA(0)2714 3089 y Fz(1)p 2582 3130 V 2582 3213 a Fs(D)2660 3187 y Fr(0)2720 3213 y Fz(+)g Fs(i\021)2900 3023 y Fp(\023)2967 3045 y Fo(l)3008 3151 y Fs(:)0 3359 y Fz(W)-8 b(e)32 b(ha)m(v)m(e)83 3576 y Fq(j)120 3547 y Fp(d)108 3576 y Fs(Q)180 3545 y FA(0)180 3606 y Fo(k)r(;l)264 3576 y Fz(\()p Fs(p;)15 b(q)s Fz(\))p Fq(j)26 b(\024)767 3515 y Fz(1)p 621 3556 336 4 v 621 3664 a(\(2)p Fs(\031)s Fz(\))791 3628 y Fr(1+)891 3601 y Fi(3)p Fg(l)p 893 3613 51 3 v 903 3654 a Fi(2)982 3453 y Fp(Z)1073 3479 y Fr(+)p FA(1)1033 3659 y(\0001)1218 3576 y Fs(d\021)1329 3453 y Fp(Z)1405 3576 y Fq(\001)15 b(\001)g(\001)1496 3453 y Fp(Z)1893 3515 y Fz(1)p 1612 3556 608 4 v 1612 3643 a(\()p Fs(E)5 b Fz(\()p Fs(p)p Fz(\))1835 3616 y Fr(2)1895 3643 y Fz(+)20 b Fs(\021)2034 3616 y Fr(2)2074 3643 y Fz(\))2109 3616 y Fr(1)p Fo(=)p Fr(2)2230 3576 y Fq(j)2272 3553 y Fp(b)2255 3576 y Fs(R)p Fz(\()p Fs(p;)15 b(p)2491 3590 y Fr(1)2531 3576 y Fz(\))p Fq(j\002)379 3889 y(\002)781 3827 y Fz(1)p 480 3868 648 4 v 480 3955 a(\()p Fs(E)5 b Fz(\()p Fs(p)668 3969 y Fr(1)708 3955 y Fz(\))743 3929 y Fr(2)803 3955 y Fz(+)20 b Fs(\021)942 3929 y Fr(2)982 3955 y Fz(\))1017 3929 y Fr(1)p Fo(=)p Fr(4)1152 3775 y Fo(k)r FA(\000)p Fr(1)1159 3802 y Fp(Y)1155 3998 y Fo(j)t Fr(=1)1296 3761 y Fp(\022)1673 3827 y Fz(1)p 1373 3868 645 4 v 1373 3955 a(\()p Fs(E)5 b Fz(\()p Fs(p)1561 3969 y Fo(j)1598 3955 y Fz(\))1633 3929 y Fr(2)1693 3955 y Fz(+)20 b Fs(\021)1832 3929 y Fr(2)1872 3955 y Fz(\))1907 3929 y Fr(1)p Fo(=)p Fr(4)2027 3889 y Fq(j)2070 3866 y Fp(b)2052 3889 y Fs(R)q Fz(\()p Fs(p)2203 3903 y Fo(j)2240 3889 y Fs(;)15 b(p)2326 3903 y Fo(j)t Fr(+1)2453 3889 y Fz(\))p Fq(j)2868 3827 y Fz(1)p 2523 3868 735 4 v 2523 3955 a(\()p Fs(E)5 b Fz(\()p Fs(p)2711 3969 y Fo(j)t Fr(+1)2839 3955 y Fz(\))2874 3929 y Fr(2)2934 3955 y Fz(+)20 b Fs(\021)3073 3929 y Fr(2)3113 3955 y Fz(\))3148 3929 y Fr(1)p Fo(=)p Fr(4)3268 3761 y Fp(\023)3350 3889 y Fq(\002)676 4219 y(\002)767 4105 y Fo(n)p FA(\000)p Fr(2)776 4132 y Fp(Y)771 4330 y Fo(j)t Fr(=)p Fo(k)915 4090 y Fp(\022)1292 4157 y Fz(1)p 992 4198 645 4 v 992 4285 a(\()p Fs(E)5 b Fz(\()p Fs(p)1180 4299 y Fo(j)1217 4285 y Fz(\))1252 4259 y Fr(2)1312 4285 y Fz(+)20 b Fs(\021)1451 4259 y Fr(2)1491 4285 y Fz(\))1526 4258 y Fr(1)p Fo(=)p Fr(4)1646 4219 y Fq(j)1688 4195 y Fp(b)1671 4219 y Fs(')1730 4192 y FA(0)1755 4219 y Fz(\()p Fs(p)1836 4233 y Fo(j)1892 4219 y Fq(\000)g Fs(p)2029 4233 y Fo(j)t Fr(+1)2156 4219 y Fz(\))p Fq(j)2571 4157 y Fz(1)p 2226 4198 735 4 v 2226 4285 a(\()p Fs(E)5 b Fz(\()p Fs(p)2414 4299 y Fo(j)t Fr(+1)2542 4285 y Fz(\))2577 4259 y Fr(2)2637 4285 y Fz(+)20 b Fs(\021)2776 4259 y Fr(2)2815 4285 y Fz(\))2850 4258 y Fr(1)p Fo(=)p Fr(4)2971 4090 y Fp(\023)3053 4219 y Fq(\002)1159 4505 y(\002)1609 4444 y Fz(1)p 1260 4484 746 4 v 1260 4571 a(\()p Fs(E)5 b Fz(\()p Fs(p)1448 4585 y Fo(n)p FA(\000)p Fr(1)1586 4571 y Fz(\))1621 4545 y Fr(2)1681 4571 y Fz(+)19 b Fs(\021)1819 4545 y Fr(2)1859 4571 y Fz(\))1894 4545 y Fr(1)p Fo(=)p Fr(4)2015 4505 y Fq(j)2056 4481 y Fp(b)2040 4505 y Fs(')2099 4479 y FA(0)2123 4505 y Fz(\()p Fs(p)2204 4519 y Fo(n)p FA(\000)p Fr(1)2361 4505 y Fq(\000)h Fs(q)s Fz(\))p Fq(j)2847 4444 y 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a(E)5 b Fz(\()p Fs(\021)s Fz(\))2414 5005 y Fg(k)q Fi(+1)p 2415 5018 111 3 v 2456 5059 a(2)2566 4857 y Fp(Z)2641 4981 y Fq(\001)15 b(\001)g(\001)2732 4857 y Fp(Z)2915 4919 y Fq(j)2957 4896 y Fp(b)2940 4919 y Fs(R)q Fz(\()p Fs(p;)g(p)3177 4933 y Fr(1)3216 4919 y Fz(\))p Fq(j)p 2848 4960 496 4 v 2848 5047 a Fs(E)5 b Fz(\()p Fs(p)21 b Fz(+)f Fs(p)3159 5061 y Fr(1)3198 5047 y Fz(\))3233 5020 y Fr(1)p Fo(=)p Fr(2)3353 4981 y Fq(\002)277 5294 y(\002)368 5180 y Fo(k)r FA(\000)p Fr(1)374 5207 y Fp(Y)371 5403 y Fo(j)t Fr(=1)588 5232 y Fq(j)631 5209 y Fp(b)613 5232 y Fs(R)q Fz(\()p Fs(p)764 5246 y Fo(j)801 5232 y Fs(;)15 b(p)887 5246 y Fo(j)t Fr(+1)1014 5232 y Fz(\))p Fq(j)p 522 5273 619 4 v 522 5360 a Fs(E)5 b Fz(\()p Fs(p)675 5374 y Fo(j)732 5360 y Fz(+)20 b Fs(p)869 5374 y Fo(j)t Fr(+1)996 5360 y Fz(\))1031 5334 y Fr(1)p Fo(=)p Fr(2)1166 5180 y Fo(n)p FA(\000)p Fr(2)1174 5207 y Fp(Y)1170 5405 y Fo(j)t Fr(=)p Fo(k)1314 5166 y Fp(\022)1690 5232 y Fz(1)p 1391 5273 645 4 v 1391 5360 a(\()p Fs(E)5 b Fz(\()p Fs(p)1579 5374 y Fo(j)1616 5360 y Fz(\))1651 5334 y Fr(2)1711 5360 y Fz(+)20 b Fs(\021)1850 5334 y Fr(2)1890 5360 y Fz(\))1925 5334 y Fr(1)p Fo(=)p Fr(4)2045 5294 y Fq(j)2087 5270 y Fp(b)2070 5294 y Fs(')2129 5268 y FA(0)2153 5294 y Fz(\()p Fs(p)2234 5308 y Fo(j)2291 5294 y Fq(\000)g Fs(p)2428 5308 y Fo(j)t Fr(+1)2555 5294 y Fz(\))p Fq(j)2970 5232 y Fz(1)p 2625 5273 735 4 v 2625 5360 a(\()p Fs(E)5 b Fz(\()p Fs(p)2813 5374 y Fo(j)t Fr(+1)2941 5360 y Fz(\))2976 5334 y Fr(2)3036 5360 y Fz(+)19 b Fs(\021)3174 5334 y Fr(2)3214 5360 y Fz(\))3249 5334 y Fr(1)p Fo(=)p Fr(4)3370 5166 y Fp(\023)3452 5294 y Fq(\002)1133 5580 y(\002)1584 5519 y Fz(1)p 1234 5559 746 4 v 1234 5647 a(\()p Fs(E)5 b Fz(\()p Fs(p)1422 5661 y Fo(n)p FA(\000)p Fr(1)1560 5647 y Fz(\))1595 5620 y Fr(2)1655 5647 y Fz(+)20 b Fs(\021)1794 5620 y Fr(2)1834 5647 y Fz(\))1869 5620 y Fr(1)p Fo(=)p Fr(4)1989 5580 y Fq(j)2031 5556 y Fp(b)2014 5580 y Fs(')2073 5554 y FA(0)2097 5580 y Fz(\()p Fs(p)2178 5594 y Fo(n)p FA(\000)p Fr(1)2336 5580 y Fq(\000)g Fs(q)s Fz(\))p Fq(j)2821 5519 y Fz(1)p 2541 5559 606 4 v 2541 5647 a(\()p Fs(E)5 b Fz(\()p Fs(q)s Fz(\))2762 5620 y Fr(2)2823 5647 y Fz(+)20 b Fs(\021)2962 5620 y Fr(2)3002 5647 y Fz(\))3037 5620 y Fr(1)p Fo(=)p Fr(4)3172 5580 y Fs(dp)3265 5594 y Fr(1)3320 5580 y Fq(\001)15 b(\001)g(\001)h Fs(dp)3534 5594 y Fo(n)p FA(\000)p Fr(1)3671 5580 y Fs(:)1844 5906 y Fz(29)p eop end %%Page: 30 30 TeXDict begin 30 29 bop 0 68 a Fz(No)m(w)31 b(if)f(w)m(e)h(use)f(the)h (easy)g(generalization)i(of)d(\(18\),)414 252 y Fs(E)5 b Fz(\()p Fs(p)21 b Fq(\000)f Fs(q)s Fz(\))25 b Fq(\024)g Fs(E)5 b Fz(\()p Fs(p)21 b Fq(\000)f Fs(p)1190 266 y Fr(1)1229 252 y Fz(\))g(+)g Fs(E)5 b Fz(\()p Fs(p)1528 266 y Fr(1)1588 252 y Fq(\000)20 b Fs(p)1725 266 y Fr(2)1765 252 y Fz(\))g(+)g Fq(\001)15 b(\001)g(\001)21 b Fz(+)f Fs(E)5 b Fz(\()p Fs(p)2281 266 y Fo(n)p FA(\000)p Fr(2)2439 252 y Fq(\000)20 b Fs(p)2576 266 y Fo(n)p FA(\000)p Fr(1)2713 252 y Fz(\))g(+)g Fs(E)5 b Fz(\()p Fs(p)3012 266 y Fo(n)p FA(\000)p Fr(1)3170 252 y Fq(\000)20 b Fs(q)s Fz(\))p Fs(;)0 436 y Fz(w)m(e)31 b(obtain)g(b)m(y)f(a)h(similar)f(argumen)m(t)h (as)g(b)s(efore)83 717 y Fq(j)-15 b(j)p Fs(Q)190 680 y FA(0)190 740 y Fo(k)r(;l)274 717 y Fq(j)g(j)309 731 y FA(Q)397 717 y Fq(\024)503 656 y Fz(2)558 592 y Fg(k)q Fi(+1)p 558 605 111 3 v 598 646 a(2)p 503 696 181 4 v 543 780 a Fz(2)p Fs(\031)708 562 y Fp(")761 717 y Fs(k)s Fz(\()p Fs(C)911 731 y Fo(R)970 717 y Fz(\))1005 680 y Fo(k)1048 717 y Fz(\(4)p Fs(\031)s(C)1248 731 y FA(1)1323 717 y Fz(\))1358 680 y Fo(l)1400 562 y Fp( )1472 594 y(Z)1563 620 y FA(1)1522 800 y(\0001)1831 656 y Fs(d\021)p 1677 696 404 4 v 1677 806 a(E)5 b Fz(\()p Fs(\021)s Fz(\))1867 770 y Fo(l)q Fr(+)1954 742 y Fg(k)q Fi(+1)p 1955 755 111 3 v 1995 796 a(2)2090 562 y Fp(!)1550 1023 y Fz(+)p Fs(l)r Fz(\()p Fs(C)1750 1037 y Fo(R)1807 1023 y Fz(\))1842 986 y Fo(k)1885 1023 y Fz(\(4)p Fs(\031)s(C)2085 1037 y FA(1)2161 1023 y Fz(\))2196 986 y Fo(l)q FA(\000)p Fr(1)2313 1023 y Fs(S)2369 1037 y Fr(6)2408 1023 y Fs(C)2473 1037 y Fr(6)2527 868 y Fp( )2599 900 y(Z)2690 926 y FA(1)2650 1106 y(\0001)2920 962 y Fs(d\021)p 2804 1002 327 4 v 2804 1111 a(E)g Fz(\()p Fs(\021)s Fz(\))2994 1075 y Fo(l)q Fr(+)3081 1048 y Fg(k)p 3083 1060 34 3 v 3085 1101 a Fi(2)3141 868 y Fp(!#)3281 1023 y Fq(j)-15 b(j)p Fs(Q)p Fq(j)g(j)3423 986 y Fo(k)3423 1046 y FA(Q)3485 1023 y Fq(j)g(j)p Fs(\032)3567 986 y FA(0)3591 1023 y Fq(j)g(j)3626 986 y Fo(l)3626 1046 y FA(C)3671 1023 y Fs(:)0 1286 y Fz(T)-8 b(o)31 b(obtain)g(this)f(result,)g(w)m(e)h(ha)m(v)m(e)h (estimated)g(eac)m(h)f(term)g(con)m(taining)g(a)g Fs(')2629 1253 y FA(0)2683 1286 y Fz(b)m(y)g(using)402 1383 y Fp(\014)402 1437 y(\014)402 1492 y(\014)402 1546 y(\014)417 1383 y(\014)417 1437 y(\014)417 1492 y(\014)417 1546 y(\014)798 1453 y Fz(1)p 457 1494 728 4 v 457 1581 a(\()p Fq(j)p Fs(D)592 1595 y Fr(0)633 1581 y Fq(j)658 1555 y Fr(2)717 1581 y Fz(+)20 b Fs(E)5 b Fz(\()p Fs(\021)s Fz(\))998 1555 y Fr(2)1039 1581 y Fz(\))1074 1554 y Fr(1)p Fo(=)p Fr(4)1195 1515 y Fs(')1254 1477 y FA(0)1628 1453 y Fz(1)p 1287 1494 V 1287 1581 a(\()p Fq(j)p Fs(D)1422 1595 y Fr(0)1463 1581 y Fq(j)1488 1555 y Fr(2)1548 1581 y Fz(+)19 b Fs(E)5 b Fz(\()p Fs(\021)s Fz(\))1828 1555 y Fr(2)1869 1581 y Fz(\))1904 1554 y Fr(1)p Fo(=)p Fr(4)2025 1383 y Fp(\014)2025 1437 y(\014)2025 1492 y(\014)2025 1546 y(\014)2040 1383 y(\014)2040 1437 y(\014)2040 1492 y(\014)2040 1546 y(\014)2070 1608 y Fd(S)2127 1616 y Fl(1)2222 1515 y Fq(\024)2401 1453 y Fz(1)p 2328 1494 192 4 v 2328 1577 a Fs(E)g Fz(\()p Fs(\021)s Fz(\))2544 1437 y Fp(\014)2544 1492 y(\014)2559 1437 y(\014)2559 1492 y(\014)2590 1515 y Fs(')2649 1477 y FA(0)2672 1437 y Fp(\014)2672 1492 y(\014)2688 1437 y(\014)2688 1492 y(\014)2718 1551 y Fo(L)2766 1532 y Fl(1)2860 1515 y Fq(\024)2992 1453 y Fs(C)3057 1467 y FA(1)p 2966 1494 V 2966 1577 a Fs(E)g Fz(\()p Fs(\021)s Fz(\))3168 1515 y Fq(j)-15 b(j)p Fs(')3262 1477 y FA(0)3286 1515 y Fq(j)g(j)3321 1529 y FA(Y)0 1785 y Fz(and)30 b(when)f Fs(E)5 b Fz(\()p Fs(p)567 1799 y Fo(j)624 1785 y Fq(\000)20 b Fs(p)761 1799 y Fo(j)t Fr(+1)888 1785 y Fz(\))30 b(app)s(ears)g(in)g(fron)m(t)g(of)h(a)1814 1761 y Fp(b)1798 1785 y Fs(')1857 1759 y FA(0)1881 1785 y Fz(\()p Fs(p)1962 1799 y Fo(j)2018 1785 y Fq(\000)20 b Fs(p)2155 1799 y Fo(j)t Fr(+1)2282 1785 y Fz(\))30 b(\(i.e.)42 b(when)30 b Fs(j)g Fq(\025)25 b Fs(k)s Fz(\),)32 b(b)m(y)e(using)98 1915 y Fp(\014)98 1970 y(\014)98 2024 y(\014)98 2079 y(\014)113 1915 y(\014)113 1970 y(\014)113 2024 y(\014)113 2079 y(\014)495 1986 y Fz(1)p 154 2026 728 4 v 154 2113 a(\()p Fq(j)p Fs(D)289 2127 y Fr(0)329 2113 y Fq(j)354 2087 y Fr(2)414 2113 y Fz(+)20 b Fs(E)5 b Fz(\()p Fs(\021)s Fz(\))695 2087 y Fr(2)736 2113 y Fz(\))771 2087 y Fr(1)p Fo(=)p Fr(4)891 2047 y Fs(f)1296 1986 y Fz(1)p 955 2026 V 955 2113 a(\()p Fq(j)p Fs(D)1090 2127 y Fr(0)1130 2113 y Fq(j)1155 2087 y Fr(2)1215 2113 y Fz(+)20 b Fs(E)5 b Fz(\()p Fs(\021)s Fz(\))1496 2087 y Fr(2)1537 2113 y Fz(\))1572 2087 y Fr(1)p Fo(=)p Fr(4)1692 1915 y Fp(\014)1692 1970 y(\014)1692 2024 y(\014)1692 2079 y(\014)1708 1915 y(\014)1708 1970 y(\014)1708 2024 y(\014)1708 2079 y(\014)1738 2140 y Fd(S)1795 2148 y Fl(1)1054 2314 y Fq(\024)1150 2182 y Fp(\014)1150 2236 y(\014)1150 2291 y(\014)1150 2345 y(\014)1166 2182 y(\014)1166 2236 y(\014)1166 2291 y(\014)1166 2345 y(\014)1547 2252 y Fz(1)p 1206 2293 V 1206 2380 a(\()p Fq(j)p Fs(D)1341 2394 y Fr(0)1381 2380 y Fq(j)1406 2354 y Fr(2)1466 2380 y Fz(+)20 b Fs(E)5 b Fz(\()p Fs(\021)s Fz(\))1747 2354 y Fr(2)1788 2380 y Fz(\))1823 2353 y Fr(1)p Fo(=)p Fr(4)1943 2314 y Fs(f)2348 2252 y Fz(1)p 2007 2293 V 2007 2380 a(\()p Fq(j)p Fs(D)2142 2394 y Fr(0)2183 2380 y Fq(j)2208 2354 y Fr(2)2268 2380 y Fz(+)20 b Fs(E)5 b Fz(\()p Fs(\021)s Fz(\))2549 2354 y Fr(2)2589 2380 y Fz(\))2624 2353 y Fr(1)p Fo(=)p Fr(4)2745 2182 y Fp(\014)2745 2236 y(\014)2745 2291 y(\014)2745 2345 y(\014)2760 2182 y(\014)2760 2236 y(\014)2760 2291 y(\014)2760 2345 y(\014)2790 2407 y Fd(S)2847 2416 y Fi(6)2911 2314 y Fq(\024)3171 2252 y Fs(S)3227 2266 y Fr(6)p 3017 2293 402 4 v 3017 2380 a Fs(E)g Fz(\()p Fs(\021)s Fz(\))3207 2353 y Fr(1)p Fo(=)p Fr(2)3319 2380 y Fz(4)p Fs(\031)3444 2314 y Fq(j)-15 b(j)q Fs(f)10 b Fq(j)-16 b(j)3569 2341 y Fo(L)3617 2322 y Fi(6)3671 2314 y Fs(:)0 2558 y Fz(So)30 b(w)m(e)h(ha)m(v)m(e)220 2742 y Fq(j)-15 b(j)p Fs(Q)327 2704 y FA(0)327 2765 y Fo(k)r(;l)411 2742 y Fq(j)g(j)446 2756 y FA(Q)592 2742 y Fq(\024)82 b Fz(2)800 2676 y Fg(k)q Fi(+1)p 801 2689 111 3 v 841 2730 a(2)941 2641 y Fp(h)984 2742 y Fs(k)s Fz(\()p Fs(C)1134 2756 y Fo(R)1192 2742 y Fz(\))1227 2704 y Fo(k)1270 2742 y Fz(\(4)p Fs(\031)s(C)1470 2756 y FA(1)1546 2742 y Fz(\))1581 2704 y Fo(l)1607 2742 y Fs(K)1684 2773 y Fo(l)q Fr(+)1771 2745 y Fg(k)q Fi(+1)p 1771 2758 V 1811 2799 a(2)1916 2742 y Fz(+)20 b Fs(l)r Fz(\()p Fs(C)2136 2756 y Fo(R)2194 2742 y Fz(\))2229 2704 y Fo(k)2272 2742 y Fz(\(4)p Fs(\031)s(C)2472 2756 y FA(1)2548 2742 y Fz(\))2583 2704 y Fo(l)q FA(\000)p Fr(1)2699 2742 y Fs(S)2755 2756 y Fr(6)2795 2742 y Fs(C)2860 2756 y Fr(6)2899 2742 y Fs(K)2976 2772 y Fo(l)q Fr(+)3063 2745 y Fg(k)p 3063 2757 34 3 v 3065 2798 a Fi(2)3111 2641 y Fp(i)3169 2742 y Fq(j)-15 b(j)p Fs(Q)p Fq(j)g(j)3311 2704 y Fo(k)3311 2764 y FA(Q)3373 2742 y Fq(j)g(j)p Fs(\032)3455 2704 y FA(0)3479 2742 y Fq(j)g(j)3514 2704 y Fo(l)3514 2764 y FA(C)592 2966 y Fq(\024)82 b Fz(2)800 2901 y Fg(k)q Fi(+1)p 801 2914 111 3 v 841 2955 a(2)926 2966 y Fs(n)p Fz(\()p Fs(C)1081 2980 y Fo(R)1138 2966 y Fz(\))1173 2929 y Fo(k)1216 2966 y Fz(\(4)p Fs(\031)s(C)1416 2980 y FA(1)1492 2966 y Fz(\))1527 2929 y Fo(l)1553 2966 y Fs(K)1630 2997 y Fo(l)q Fr(+)1717 2969 y Fg(k)p 1717 2981 34 3 v 1719 3023 a Fi(2)1781 2966 y Fz(max)1965 2838 y Fp(\022)2032 2966 y Fz(1)p Fs(;)2148 2905 y(S)2204 2919 y Fr(6)2243 2905 y Fs(C)2308 2919 y Fr(6)p 2128 2945 241 4 v 2128 3028 a Fz(4)p Fs(\031)s(C)2293 3042 y FA(1)2378 2838 y Fp(\023)2460 2966 y Fq(j)-15 b(j)p Fs(Q)p Fq(j)g(j)2602 2929 y Fo(k)2602 2989 y FA(Q)2664 2966 y Fq(j)g(j)p Fs(\032)2746 2929 y FA(0)2770 2966 y Fq(j)g(j)2805 2929 y Fo(l)2805 2989 y FA(C)0 3195 y Fz(whic)m(h)30 b(implies)553 3423 y Fq(j)-15 b(j)p Fs(Q)660 3438 y Fo(k)r(;l)745 3423 y Fq(j)g(j)780 3437 y FA(Q)867 3423 y Fq(\024)25 b Fz(\()998 3386 y Fo(n)998 3446 y(k)1045 3423 y Fz(\))16 b(2)1151 3358 y Fg(k)q Fi(+1)p 1151 3371 111 3 v 1192 3412 a(2)1276 3423 y Fs(n)p Fz(\()p Fs(C)1431 3437 y Fo(R)1489 3423 y Fz(\))1524 3386 y Fo(k)1567 3423 y Fz(\(4)p Fs(\031)s(C)1767 3437 y FA(1)1843 3423 y Fz(\))1878 3386 y Fo(l)1904 3423 y Fs(K)1981 3454 y Fo(l)q Fr(+)2068 3427 y Fg(k)p 2068 3439 34 3 v 2070 3480 a Fi(2)2131 3423 y Fz(max)2315 3295 y Fp(\022)2382 3423 y Fz(1)p Fs(;)2499 3362 y(S)2555 3376 y Fr(6)2594 3362 y Fs(C)2659 3376 y Fr(6)p 2478 3402 241 4 v 2478 3486 a Fz(4)p Fs(\031)s(C)2643 3500 y FA(1)2728 3295 y Fp(\023)2810 3423 y Fq(j)-15 b(j)p Fs(Q)p Fq(j)g(j)2952 3386 y Fo(k)2952 3446 y FA(Q)3015 3423 y Fq(j)g(j)p Fs(\032)3097 3386 y FA(0)3120 3423 y Fq(j)g(j)3155 3386 y Fo(l)3155 3446 y FA(C)3201 3423 y Fs(:)0 3738 y Fq(\017)61 b Fs(Q)178 3752 y Fr(0)p Fo(;n)312 3738 y Fy(with)34 b Fs(n)25 b Fq(\025)g Fz(3.)41 b(Recall)32 b(that)930 3981 y Fs(Q)1002 3995 y Fr(0)p Fo(;n)1129 3981 y Fz(=)1235 3920 y(\()p Fq(\000)p Fz(1\))1421 3887 y Fo(n)p Fr(+1)p 1235 3960 325 4 v 1346 4044 a Fz(2)p Fs(\031)1584 3857 y Fp(Z)1675 3884 y Fr(+)p FA(1)1634 4064 y(\0001)1819 3981 y Fs(d\021)2056 3920 y Fz(1)p 1924 3960 309 4 v 1924 4044 a Fs(D)2002 4017 y Fr(0)2063 4044 y Fz(+)19 b Fs(i\021)2258 3853 y Fp(\022)2325 3981 y Fs(')2384 3944 y FA(0)2549 3920 y Fz(1)p 2418 3960 V 2418 4044 a Fs(D)2496 4017 y Fr(0)2555 4044 y Fz(+)h Fs(i\021)2736 3853 y Fp(\023)2803 3876 y Fo(n)0 4213 y Fz(so)31 b(that)83 4454 y Fs(E)5 b Fz(\()p Fs(p)21 b Fq(\000)f Fs(q)s Fz(\))p Fs(E)5 b Fz(\()p Fs(p)20 b Fz(+)g Fs(q)s Fz(\))770 4417 y Fr(1)p Fo(=)p Fr(2)881 4454 y Fq(j)927 4432 y Fp(d)906 4454 y Fs(Q)978 4468 y Fr(0)p Fo(;n)1080 4454 y Fz(\()p Fs(p;)15 b(q)s Fz(\))p Fq(j)26 b(\024)1442 4393 y Fs(E)5 b Fz(\()p Fs(p)21 b Fq(\000)e Fs(q)s Fz(\))p 1437 4434 355 4 v 1437 4540 a(\(2)p Fs(\031)s Fz(\))1607 4504 y Fr(1+)1707 4477 y Fi(3)p Fg(n)p 1708 4489 69 3 v 1727 4530 a Fi(2)1816 4331 y Fp(Z)1907 4357 y Fr(+)p FA(1)1867 4537 y(\0001)2137 4393 y Fs(d\021)p 2062 4434 246 4 v 2062 4540 a(E)5 b Fz(\()p Fs(\021)s Fz(\))2262 4477 y Fi(1)p 2263 4489 31 3 v 2263 4530 a(2)2333 4331 y Fp(Z)2408 4454 y Fq(\001)15 b(\001)g(\001)2499 4331 y Fp(Z)2621 4454 y Fs(dp)2714 4468 y Fr(1)2768 4454 y Fq(\001)g(\001)g(\001)h Fs(dp)2982 4468 y Fo(n)p FA(\000)p Fr(1)3120 4454 y Fq(\002)31 4761 y(\002)537 4700 y(j)578 4676 y Fp(b)562 4700 y Fs(')621 4673 y FA(0)645 4700 y Fz(\()p Fs(p)k Fq(\000)g Fs(p)883 4714 y Fr(1)922 4700 y Fz(\))p Fq(j)p 132 4740 1256 4 v 132 4827 a Fz(\()p Fs(E)5 b Fz(\()p Fs(p)p Fz(\))355 4801 y Fr(2)416 4827 y Fz(+)20 b Fs(\021)555 4801 y Fr(2)594 4827 y Fz(\))629 4801 y Fr(1)p Fo(=)p Fr(4)740 4827 y Fz(\()p Fs(E)5 b Fz(\()p Fs(p)928 4841 y Fr(1)968 4827 y Fz(\))1003 4801 y Fr(2)1063 4827 y Fz(+)20 b Fs(\021)1202 4801 y Fr(2)1242 4827 y Fz(\))1277 4801 y Fr(1)p Fo(=)p Fr(4)1412 4647 y Fo(n)p FA(\000)p Fr(2)1421 4675 y Fp(Y)1417 4870 y Fo(j)t Fr(=1)1560 4633 y Fp(\022)1937 4700 y Fz(1)p 1637 4740 645 4 v 1637 4827 a(\()p Fs(E)5 b Fz(\()p Fs(p)1825 4841 y Fo(j)1863 4827 y Fz(\))1898 4801 y Fr(2)1958 4827 y Fz(+)19 b Fs(\021)2096 4801 y Fr(2)2136 4827 y Fz(\))2171 4801 y Fr(1)p Fo(=)p Fr(4)2292 4761 y Fq(j)2333 4737 y Fp(b)2317 4761 y Fs(')2376 4735 y FA(0)2400 4761 y Fz(\()p Fs(p)2481 4775 y Fo(j)2537 4761 y Fq(\000)h Fs(p)2674 4775 y Fo(j)t Fr(+1)2801 4761 y Fz(\))p Fq(j)3216 4700 y Fz(1)p 2871 4740 735 4 v 2871 4827 a(\()p Fs(E)5 b Fz(\()p Fs(p)3059 4841 y Fo(j)t Fr(+1)3187 4827 y Fz(\))3222 4801 y Fr(2)3282 4827 y Fz(+)20 b Fs(\021)3421 4801 y Fr(2)3461 4827 y Fz(\))3496 4801 y Fr(1)p Fo(=)p Fr(4)3616 4633 y Fp(\023)3698 4761 y Fq(\002)1648 5045 y(\002)2098 4984 y Fz(1)p 1749 5024 746 4 v 1749 5112 a(\()p Fs(E)5 b Fz(\()p Fs(p)1937 5126 y Fo(n)p FA(\000)p Fr(1)2074 5112 y Fz(\))2109 5085 y Fr(2)2169 5112 y Fz(+)20 b Fs(\021)2308 5085 y Fr(2)2348 5112 y Fz(\))2383 5085 y Fr(1)p Fo(=)p Fr(4)2504 5045 y Fq(j)2545 5021 y Fp(b)2529 5045 y Fs(')2588 5019 y FA(0)2612 5045 y Fz(\()p Fs(p)2693 5059 y Fo(n)p FA(\000)p Fr(1)2850 5045 y Fq(\000)g Fs(q)s Fz(\))p Fq(j)3336 4984 y Fz(1)p 3055 5024 606 4 v 3055 5112 a(\()p Fs(E)5 b Fz(\()p Fs(q)s Fz(\))3276 5085 y Fr(2)3337 5112 y Fz(+)20 b Fs(\021)3476 5085 y Fr(2)3516 5112 y Fz(\))3551 5085 y Fr(1)p Fo(=)p Fr(4)3671 5045 y Fs(:)0 5282 y Fz(W)-8 b(e)32 b(no)m(w)e(use)g(\(46\))i(to)f(b)s(ound)d(for)j(some)f Fs(f)1498 5296 y Fr(1)1537 5282 y Fz(,)h Fs(f)1638 5296 y Fr(2)1707 5282 y Fz(and)f Fs(f)1929 5296 y Fr(3)494 5384 y Fp(\014)494 5438 y(\014)494 5493 y(\014)494 5547 y(\014)494 5602 y(\014)494 5656 y(\014)509 5384 y(\014)509 5438 y(\014)509 5493 y(\014)509 5547 y(\014)509 5602 y(\014)509 5656 y(\014)583 5456 y Fr(3)542 5484 y Fp(Y)539 5679 y Fo(j)t Fr(=1)677 5442 y Fp(\022)1023 5508 y Fz(1)p 754 5549 585 4 v 754 5636 a(\()p Fq(j)p Fs(D)889 5650 y Fr(0)929 5636 y Fq(j)954 5610 y Fr(2)1014 5636 y Fz(+)20 b Fs(\021)1153 5610 y Fr(2)1193 5636 y Fz(\))1228 5610 y Fr(1)p Fo(=)p Fr(4)1348 5570 y Fs(f)1393 5584 y Fo(j)1708 5508 y Fz(1)p 1439 5549 V 1439 5636 a(\()p Fq(j)p Fs(D)1574 5650 y Fr(0)1614 5636 y Fq(j)1639 5610 y Fr(2)1699 5636 y Fz(+)g Fs(\021)1838 5610 y Fr(2)1878 5636 y Fz(\))1913 5610 y Fr(1)p Fo(=)p Fr(4)2033 5442 y Fp(\023)2100 5384 y(\014)2100 5438 y(\014)2100 5493 y(\014)2100 5547 y(\014)2100 5602 y(\014)2100 5656 y(\014)2115 5384 y(\014)2115 5438 y(\014)2115 5493 y(\014)2115 5547 y(\014)2115 5602 y(\014)2115 5656 y(\014)2145 5715 y Fd(S)2202 5696 y Fi(2)2267 5570 y Fq(\024)2526 5508 y Fz(\()p Fs(S)2617 5522 y Fr(6)2656 5508 y Fz(\))2691 5475 y Fr(3)p 2373 5549 513 4 v 2373 5636 a Fs(E)5 b Fz(\()p Fs(\021)s Fz(\))2563 5610 y Fr(3)p Fo(=)p Fr(2)2674 5636 y Fz(\(4)p Fs(\031)s Fz(\))2844 5610 y Fr(3)2953 5456 y(3)2913 5484 y Fp(Y)2910 5679 y Fo(j)t Fr(=1)3047 5570 y Fq(j)-14 b(j)p Fs(f)3128 5584 y Fo(j)3164 5570 y Fq(j)f(j)3199 5601 y Fo(L)3247 5582 y Fi(6)3618 5570 y Fz(\(48\))1844 5906 y(30)p eop end %%Page: 31 31 TeXDict begin 31 30 bop 0 63 a Fz(to)31 b(obtain)679 215 y Fq(j)-15 b(j)p Fs(Q)786 229 y Fr(0)p Fo(;n)888 215 y Fq(j)g(j)923 229 y FA(Q)1010 215 y Fq(\024)25 b Fs(n)1171 79 y Fq(p)p 1247 79 46 4 v 75 x Fz(2)p 1171 194 122 4 v 1181 278 a(2)p Fs(\031)1317 87 y Fp(\022)1384 92 y(Z)1475 118 y FA(1)1435 298 y(\0001)1778 154 y Fs(d\021)p 1589 194 474 4 v 1589 282 a(E)5 b Fz(\()p Fs(\021)s Fz(\))1779 255 y Fr(2+\()p Fo(n)p FA(\000)p Fr(3\))2073 87 y Fp(\023)2155 215 y Fz(\()p Fs(S)2246 229 y Fr(6)2285 215 y Fs(C)2350 229 y Fr(6)2390 215 y Fz(\))2425 178 y Fr(3)2465 215 y Fz(\(4)p Fs(\031)s(C)2665 229 y FA(1)2740 215 y Fz(\))2775 178 y Fo(n)p FA(\000)p Fr(3)2913 215 y Fq(j)-15 b(j)p Fs(\032)2995 178 y FA(0)3018 215 y Fq(j)g(j)3053 178 y Fo(n)3053 238 y FA(C)0 392 y Fz(or)995 505 y Fq(j)g(j)p Fs(Q)1102 519 y Fr(0)p Fo(;n)1205 505 y Fq(j)g(j)1240 519 y FA(Q)1327 505 y Fq(\024)25 b Fs(nK)1555 519 y Fo(n)p FA(\000)p Fr(1)1692 425 y Fq(p)p 1768 425 46 4 v 80 x Fz(2\()p Fs(S)1904 519 y Fr(6)1944 505 y Fs(C)2009 519 y Fr(6)2048 505 y Fz(\))2083 467 y Fr(3)2123 505 y Fz(\(4)p Fs(\031)s(C)2323 519 y FA(1)2398 505 y Fz(\))2433 467 y Fo(n)p FA(\000)p Fr(3)2571 505 y Fq(j)-15 b(j)p Fs(\032)2653 467 y FA(0)2676 505 y Fq(j)g(j)2711 467 y Fo(n)2711 527 y FA(C)2759 505 y Fs(:)141 657 y Fz(Finally)-8 b(,)32 b(w)m(e)f(can)g(write)f(for)g(instance)h(\(recall)h(that)f Fs(C)2034 671 y FA(1)2134 657 y Fz(=)25 b(1)p Fs(=)p Fz(\(2)2400 592 y Fq(p)p 2478 592 56 4 v 2478 657 a Fs(\031)s Fz(\)\))970 858 y Fq(j)-15 b(j)p Fs(Q)1077 872 y Fo(n)1124 858 y Fq(j)g(j)1159 872 y FA(Q)1247 858 y Fq(\024)25 b Fs(nK)1475 877 y Fo(n=)p Fr(2)1592 858 y Fs(C)1657 872 y Fo(Q)1732 757 y Fp(\020)1786 858 y Fs(C)1851 872 y Fo(R)1909 778 y Fq(p)p 1985 778 46 4 v 80 x Fz(2)p Fq(j)-15 b(j)p Fs(Q)p Fq(j)g(j)2172 872 y FA(Q)2255 858 y Fz(+)20 b(2)2391 788 y Fq(p)p 2467 788 56 4 v 70 x Fs(\031)s Fq(j)-15 b(j)p Fs(\032)2604 821 y FA(0)2628 858 y Fq(j)g(j)2663 872 y FA(C)2708 757 y Fp(\021)2762 780 y Fo(n)3618 858 y Fz(\(49\))0 1051 y(where)826 1219 y Fs(C)891 1233 y Fo(Q)976 1219 y Fz(=)1072 1139 y Fq(p)p 1148 1139 46 4 v 80 x Fz(2)15 b(max)1392 1063 y Fp( )1464 1219 y Fz(1)p Fs(;)1581 1157 y(S)1637 1171 y Fr(6)1676 1157 y Fs(C)1741 1171 y Fr(6)p 1560 1198 241 4 v 1560 1281 a Fz(4)p Fs(\031)s(C)1725 1295 y FA(1)1810 1219 y Fs(;)1850 1091 y Fp(\022)1948 1157 y Fs(S)2004 1171 y Fr(6)2043 1157 y Fs(C)2108 1171 y Fr(6)p 1928 1198 V 1928 1281 a Fz(4)p Fs(\031)s(C)2093 1295 y FA(1)2178 1091 y Fp(\023)2245 1113 y Fr(3)2284 1063 y Fp(!)2382 1219 y Fz(=)2477 1139 y Fq(p)p 2553 1139 46 4 v 80 x Fz(2)2609 1157 y(\()p Fs(S)2700 1171 y Fr(6)2739 1157 y Fs(C)2804 1171 y Fr(6)2844 1157 y Fz(\))2879 1124 y Fr(3)p 2609 1198 310 4 v 2658 1285 a Fz(8)p Fs(\031)2758 1259 y Fr(3)p Fo(=)p Fr(2)2928 1219 y Fs(;)0 1443 y Fz(and)30 b(since)g Fs(K)476 1462 y Fo(n=)p Fr(2)619 1443 y Fq(\025)25 b Fs(K)792 1457 y Fo(n)p FA(\000)p Fr(1)960 1443 y Fz(when)k Fs(n)c Fq(\025)g Fz(2.)0 1637 y Fe(Step)35 b(2)g(:)46 b(Estimates)34 b(on)i(the)e(densit)m(y)h Fs(\032)1620 1651 y Fo(n)1667 1637 y Fe(.)0 1750 y Fq(\017)63 b Fs(\032)155 1765 y Fo(k)r(;l)273 1750 y Fy(with)35 b Fs(k)30 b Fq(\025)d Fz(2)34 b Fy(and)h Fs(n)26 b Fq(\025)h Fz(3.)45 b(As)32 b(b)s(efore)f(w)m(e)h(treat)g(for)g(instance)g(the)g(densit)m(y)f Fs(\032)2981 1717 y FA(0)2981 1778 y Fo(k)r(;l)3097 1750 y Fz(of)h(the)f Fs(Q)3431 1717 y FA(0)3431 1778 y Fo(k)r(;l)3547 1750 y Fz(where)0 1875 y(the)c Fs(k)j(R)q Fz('s)d(are)g(on)g(the)g (left)h(and)e(the)h Fs(l)i(')1409 1842 y FA(0)1433 1875 y Fz('s)e(are)g(on)g(the)g(righ)m(t.)40 b(F)-8 b(or)28 b(some)f(\014xed)g Fs(\020)k Fq(2)25 b(C)3010 1842 y FA(0)3047 1875 y Fq(\\)13 b Fs(L)3183 1842 y Fr(2)3222 1875 y Fz(,)28 b(w)m(e)g(in)m(tro)s(duce)0 1987 y Fs(Q)72 2002 y Fo(\020)137 1987 y Fz(:=)d Fs(Q)330 1955 y FA(0)330 2015 y Fo(k)r(;l)414 1987 y Fs(\020)7 b Fz(.)40 b(W)-8 b(e)32 b(th)m(us)e(estimate)83 2262 y Fq(j)118 2239 y Fp(c)108 2262 y Fs(Q)180 2277 y Fo(\020)220 2262 y Fz(\()p Fs(p;)15 b(p)p Fz(\))p Fq(j)26 b(\024)787 2200 y Fz(1)p 579 2241 461 4 v 579 2358 a(\(2)p Fs(\031)s Fz(\))749 2323 y Fr(1+)849 2289 y Fi(3\()p Fg(l)p Fi(+1\))p 850 2307 176 3 v 923 2349 a(2)1065 2138 y Fp(Z)1156 2164 y Fr(+)p FA(1)1115 2344 y(\0001)1301 2262 y Fs(d\021)1411 2138 y Fp(Z)1487 2262 y Fq(\001)15 b(\001)g(\001)1578 2138 y Fp(Z)1975 2200 y Fz(1)p 1694 2241 608 4 v 1694 2328 a(\()p Fs(E)5 b Fz(\()p Fs(p)p Fz(\))1917 2302 y Fr(2)1978 2328 y Fz(+)20 b Fs(\021)2117 2302 y Fr(2)2157 2328 y Fz(\))2192 2301 y Fr(1)p Fo(=)p Fr(4)2312 2262 y Fq(j)2354 2239 y Fp(b)2337 2262 y Fs(R)q Fz(\()p Fs(p;)15 b(p)2574 2276 y Fr(1)2614 2262 y Fz(\))p Fq(j\002)379 2583 y(\002)781 2522 y Fz(1)p 480 2562 648 4 v 480 2649 a(\()p Fs(E)5 b Fz(\()p Fs(p)668 2663 y Fr(1)708 2649 y Fz(\))743 2623 y Fr(2)803 2649 y Fz(+)20 b Fs(\021)942 2623 y Fr(2)982 2649 y Fz(\))1017 2623 y Fr(1)p Fo(=)p Fr(4)1152 2470 y Fo(k)r FA(\000)p Fr(1)1159 2497 y Fp(Y)1155 2692 y Fo(j)t Fr(=1)1296 2455 y Fp(\022)1673 2522 y Fz(1)p 1373 2562 645 4 v 1373 2649 a(\()p Fs(E)5 b Fz(\()p Fs(p)1561 2663 y Fo(j)1598 2649 y Fz(\))1633 2623 y Fr(2)1693 2649 y Fz(+)20 b Fs(\021)1832 2623 y Fr(2)1872 2649 y Fz(\))1907 2623 y Fr(1)p Fo(=)p Fr(4)2027 2583 y Fq(j)2070 2560 y Fp(b)2052 2583 y Fs(R)q Fz(\()p Fs(p)2203 2597 y Fo(j)2240 2583 y Fs(;)15 b(p)2326 2597 y Fo(j)t Fr(+1)2453 2583 y Fz(\))p Fq(j)2868 2522 y Fz(1)p 2523 2562 735 4 v 2523 2649 a(\()p Fs(E)5 b Fz(\()p Fs(p)2711 2663 y Fo(j)t Fr(+1)2839 2649 y Fz(\))2874 2623 y Fr(2)2934 2649 y Fz(+)20 b Fs(\021)3073 2623 y Fr(2)3113 2649 y Fz(\))3148 2623 y Fr(1)p Fo(=)p Fr(4)3268 2455 y Fp(\023)3350 2583 y Fq(\002)676 2913 y(\002)767 2799 y Fo(n)p FA(\000)p Fr(1)776 2827 y Fp(Y)771 3024 y Fo(j)t Fr(=)p Fo(k)915 2785 y Fp(\022)1292 2851 y Fz(1)p 992 2892 645 4 v 992 2979 a(\()p Fs(E)5 b Fz(\()p Fs(p)1180 2993 y Fo(j)1217 2979 y Fz(\))1252 2953 y Fr(2)1312 2979 y Fz(+)20 b Fs(\021)1451 2953 y Fr(2)1491 2979 y Fz(\))1526 2953 y Fr(1)p Fo(=)p Fr(4)1646 2913 y Fq(j)1688 2889 y Fp(b)1671 2913 y Fs(')1730 2887 y FA(0)1755 2913 y Fz(\()p Fs(p)1836 2927 y Fo(j)1892 2913 y Fq(\000)g Fs(p)2029 2927 y Fo(j)t Fr(+1)2156 2913 y Fz(\))p Fq(j)2571 2851 y Fz(1)p 2226 2892 735 4 v 2226 2979 a(\()p Fs(E)5 b Fz(\()p Fs(p)2414 2993 y Fo(j)t Fr(+1)2542 2979 y Fz(\))2577 2953 y Fr(2)2637 2979 y Fz(+)20 b Fs(\021)2776 2953 y Fr(2)2815 2979 y Fz(\))2850 2953 y Fr(1)p Fo(=)p Fr(4)2971 2785 y Fp(\023)3053 2913 y Fq(\002)1436 3200 y(\002)1842 3138 y Fz(1)p 1537 3179 655 4 v 1537 3266 a(\()p Fs(E)5 b Fz(\()p Fs(p)1725 3280 y Fo(n)1773 3266 y Fz(\))1808 3239 y Fr(2)1868 3266 y Fz(+)20 b Fs(\021)2007 3239 y Fr(2)2047 3266 y Fz(\))2082 3239 y Fr(1)p Fo(=)p Fr(4)2202 3200 y Fq(j)2233 3176 y Fp(b)2227 3200 y Fs(\020)7 b Fz(\()p Fs(p)2355 3214 y Fo(n)2422 3200 y Fq(\000)20 b Fs(p)p Fz(\))p Fq(j)2911 3138 y Fz(1)p 2629 3179 608 4 v 2629 3266 a(\()p Fs(E)5 b Fz(\()p Fs(p)p Fz(\))2852 3239 y Fr(2)2913 3266 y Fz(+)20 b Fs(\021)3052 3239 y Fr(2)3092 3266 y Fz(\))3127 3239 y Fr(1)p Fo(=)p Fr(4)3262 3200 y Fs(dp)3355 3214 y Fr(1)3410 3200 y Fq(\001)15 b(\001)g(\001)h Fs(dp)3624 3214 y Fo(n)3671 3200 y Fs(:)0 3423 y Fz(W)-8 b(e)32 b(no)m(w)e(use)g(as)h(b)s(efore)471 3645 y Fq(j)502 3621 y Fp(b)496 3645 y Fs(\020)7 b Fz(\()p Fs(p)624 3659 y Fo(n)691 3645 y Fq(\000)20 b Fs(p)p Fz(\))p Fq(j)25 b(\024)1019 3583 y(j)1050 3559 y Fp(b)1044 3583 y Fs(\020)7 b Fz(\()p Fs(p)1172 3597 y Fo(n)1239 3583 y Fq(\000)20 b Fs(p)p Fz(\))p Fq(j)p 1019 3624 418 4 v 1031 3707 a Fs(E)5 b Fz(\()p Fs(p)1184 3721 y Fo(n)1252 3707 y Fq(\000)20 b Fs(p)p Fz(\))1447 3571 y Fp(\000)1488 3645 y Fs(E)5 b Fz(\()p Fs(p)21 b Fq(\000)f Fs(p)1799 3659 y Fr(1)1838 3645 y Fz(\))g(+)g Fs(E)5 b Fz(\()p Fs(p)2137 3659 y Fr(1)2197 3645 y Fq(\000)20 b Fs(p)2334 3659 y Fr(2)2374 3645 y Fz(\))g(+)g Fq(\001)15 b(\001)g(\001)21 b Fz(+)f Fs(E)5 b Fz(\()p Fs(p)2890 3659 y Fo(n)p FA(\000)p Fr(1)3048 3645 y Fq(\000)20 b Fs(p)3185 3659 y Fo(n)3232 3645 y Fz(\))3267 3571 y Fp(\001)0 3864 y Fz(to)31 b(obtain)405 4094 y Fq(jh)p Fs(\032)512 4057 y FA(0)512 4117 y Fo(k)r(;l)597 4094 y Fs(;)15 b(\020)7 b Fq(ij)25 b(\024)g Fs(n)930 4033 y Fz(2)975 4000 y Fo(k)r(=)p Fr(2)1089 4033 y Fs(S)1145 4047 y Fr(6)1184 4033 y Fs(C)1249 4047 y Fr(6)p 930 4073 359 4 v 1059 4157 a Fz(4)p Fs(\031)1298 4094 y Fz(\()p Fs(C)1398 4108 y Fo(R)1456 4094 y Fz(\))1491 4057 y Fo(k)1534 4094 y Fz(\(4)p Fs(\031)s(C)1734 4108 y FA(1)1810 4094 y Fz(\))1845 4057 y Fo(l)1886 3939 y Fp( )1996 4033 y Fz(1)p 1968 4073 101 4 v 1968 4157 a(2)p Fs(\031)2094 3971 y Fp(Z)2185 3997 y FA(1)2144 4177 y(\0001)2453 4033 y Fs(d\021)p 2299 4073 404 4 v 2299 4183 a(E)5 b Fz(\()p Fs(\021)s Fz(\))2489 4147 y Fo(l)q Fr(+)2576 4119 y Fg(k)q Fi(+1)p 2577 4132 111 3 v 2618 4173 a(2)2712 3939 y Fp(!)2799 4094 y Fq(j)-15 b(j)p Fs(Q)p Fq(j)g(j)2941 4057 y Fo(k)2941 4117 y FA(Q)3004 4094 y Fq(j)g(j)p Fs(\032)3086 4057 y FA(0)3109 4094 y Fq(j)g(j)3144 4057 y Fo(l)3144 4117 y FA(C)3190 4094 y Fq(j)g(j)p Fs(\020)7 b Fq(j)-15 b(j)3307 4110 y FA(C)3348 4091 y Fl(0)0 4342 y Fz(and)30 b(so)795 4474 y Fq(j)-15 b(j)p Fs(\032)877 4489 y Fo(k)r(;l)962 4474 y Fq(j)g(j)997 4488 y FA(C)1067 4474 y Fq(\024)25 b Fs(n)15 b Fz(\()1268 4437 y Fo(n)1268 4497 y(k)1315 4474 y Fz(\))1376 4413 y Fs(S)1432 4427 y Fr(6)1471 4413 y Fs(C)1536 4427 y Fr(6)p 1376 4453 200 4 v 1425 4536 a Fz(4)p Fs(\031)1585 4474 y Fz(\()p Fs(C)1685 4488 y Fo(R)1743 4394 y Fq(p)p 1819 4394 46 4 v 80 x Fz(2)q(\))1900 4437 y Fo(k)1943 4474 y Fz(\(4)p Fs(\031)s(C)2143 4488 y FA(1)2218 4474 y Fz(\))2253 4437 y Fo(l)2280 4474 y Fs(K)2357 4505 y Fo(l)q Fr(+)2444 4477 y Fg(k)q Fi(+1)p 2444 4490 111 3 v 2484 4531 a(2)2569 4474 y Fq(j)-15 b(j)p Fs(Q)p Fq(j)g(j)2711 4437 y Fo(k)2711 4497 y FA(Q)2773 4474 y Fq(j)g(j)p Fs(\032)2855 4437 y FA(0)2879 4474 y Fq(j)g(j)2914 4437 y Fo(l)2914 4497 y FA(C)2959 4474 y Fs(:)0 4728 y Fq(\017)61 b Fs(\032)153 4743 y Fr(1)p Fo(;l)266 4728 y Fy(with)34 b Fs(l)27 b Fq(\025)e Fz(2.)41 b(W)-8 b(e)32 b(ma)m(y)f(treat)g(for)f(instance)h(with)f(the)h(same)g (notation)g(as)g(b)s(efore)83 4989 y Fq(j)118 4966 y Fp(c)108 4989 y Fs(Q)180 5004 y Fo(\020)220 4989 y Fz(\()p Fs(p;)15 b(p)p Fz(\))p Fq(j)26 b(\024)733 4928 y Fz(1)p 579 4969 355 4 v 579 5075 a(\(2)p Fs(\031)s Fz(\))749 5039 y Fr(1+)849 5012 y Fi(3)p Fg(n)p 850 5024 69 3 v 869 5065 a Fi(2)958 4866 y Fp(Z)1049 4892 y Fr(+)p FA(1)1009 5072 y(\0001)1194 4989 y Fs(d\021)1305 4866 y Fp(Z)1381 4989 y Fq(\001)15 b(\001)g(\001)1471 4866 y Fp(Z)1869 4928 y Fz(1)p 1587 4969 608 4 v 1587 5056 a(\()p Fs(E)5 b Fz(\()p Fs(p)p Fz(\))1810 5029 y Fr(2)1871 5056 y Fz(+)20 b Fs(\021)2010 5029 y Fr(2)2050 5056 y Fz(\))2085 5029 y Fr(1)p Fo(=)p Fr(4)2205 4989 y Fq(j)2248 4966 y Fp(b)2230 4989 y Fs(R)q Fz(\()p Fs(p;)15 b(p)2467 5003 y Fr(1)2507 4989 y Fz(\))p Fq(j\002)335 5296 y(\002)737 5235 y Fz(1)p 436 5275 648 4 v 436 5362 a(\()p Fs(E)5 b Fz(\()p Fs(p)624 5376 y Fr(1)664 5362 y Fz(\))699 5336 y Fr(2)759 5362 y Fz(+)20 b Fs(\021)898 5336 y Fr(2)938 5362 y Fz(\))973 5336 y Fr(1)p Fo(=)p Fr(4)1108 5182 y Fo(n)p FA(\000)p Fr(1)1117 5210 y Fp(Y)1114 5405 y Fo(j)t Fr(=1)1256 5168 y Fp(\022)1633 5235 y Fz(1)p 1333 5275 645 4 v 1333 5362 a(\()p Fs(E)5 b Fz(\()p Fs(p)1521 5376 y Fo(j)1559 5362 y Fz(\))1594 5336 y Fr(2)1654 5362 y Fz(+)20 b Fs(\021)1793 5336 y Fr(2)1832 5362 y Fz(\))1867 5336 y Fr(1)p Fo(=)p Fr(4)1988 5296 y Fq(j)2029 5272 y Fp(b)2013 5296 y Fs(')2072 5270 y FA(0)2096 5296 y Fz(\()p Fs(p)2177 5310 y Fo(j)2234 5296 y Fq(\000)f Fs(p)2370 5310 y Fo(j)t Fr(+1)2497 5296 y Fz(\))p Fq(j)2912 5235 y Fz(1)p 2567 5275 735 4 v 2567 5362 a(\()p Fs(E)5 b Fz(\()p Fs(p)2755 5376 y Fo(j)t Fr(+1)2883 5362 y Fz(\))2918 5336 y Fr(2)2978 5362 y Fz(+)20 b Fs(\021)3117 5336 y Fr(2)3157 5362 y Fz(\))3192 5336 y Fr(1)p Fo(=)p Fr(4)3312 5168 y Fp(\023)3394 5296 y Fq(\002)1436 5580 y(\002)1842 5519 y Fz(1)p 1537 5559 655 4 v 1537 5647 a(\()p Fs(E)5 b Fz(\()p Fs(p)1725 5661 y Fo(n)1773 5647 y Fz(\))1808 5620 y Fr(2)1868 5647 y Fz(+)20 b Fs(\021)2007 5620 y Fr(2)2047 5647 y Fz(\))2082 5620 y Fr(1)p Fo(=)p Fr(4)2202 5580 y Fq(j)2233 5556 y Fp(b)2227 5580 y Fs(\020)7 b Fz(\()p Fs(p)2355 5594 y Fo(n)2422 5580 y Fq(\000)20 b Fs(p)p Fz(\))p Fq(j)2911 5519 y Fz(1)p 2629 5559 608 4 v 2629 5647 a(\()p Fs(E)5 b Fz(\()p Fs(p)p Fz(\))2852 5620 y Fr(2)2913 5647 y Fz(+)20 b Fs(\021)3052 5620 y Fr(2)3092 5647 y Fz(\))3127 5620 y Fr(1)p Fo(=)p Fr(4)3262 5580 y Fs(dp)3355 5594 y Fr(1)3410 5580 y Fq(\001)15 b(\001)g(\001)h Fs(dp)3624 5594 y Fo(n)3671 5580 y Fs(:)1844 5906 y Fz(31)p eop end %%Page: 32 32 TeXDict begin 32 31 bop 0 68 a Fz(W)-8 b(e)32 b(no)m(w)e(use)g(\(48\))i (and)e(obtain)360 336 y Fq(jh)p Fs(\032)467 298 y FA(0)467 359 y Fr(1)p Fo(;l)548 336 y Fs(;)15 b(\020)7 b Fq(i)q(j)25 b(\024)g Fs(n)882 274 y Fz(2)927 241 y Fr(1)p Fo(=)p Fr(2)1037 274 y Fz(\()p Fs(S)1128 288 y Fr(6)1168 274 y Fs(C)1233 288 y Fr(6)1272 274 y Fz(\))1307 241 y Fr(3)p 882 315 466 4 v 1064 398 a Fz(4)p Fs(\031)1357 336 y(C)1422 350 y Fo(R)1479 336 y Fz(\(4)p Fs(\031)s(C)1679 350 y FA(1)1755 336 y Fz(\))1790 298 y Fo(l)q FA(\000)p Fr(2)1922 180 y Fp( )2031 274 y Fz(1)p 2004 315 101 4 v 2004 398 a(2)p Fs(\031)2129 212 y Fp(Z)2220 238 y FA(1)2180 418 y(\0001)2493 274 y Fs(d\021)p 2335 315 413 4 v 2335 421 a(E)5 b Fz(\()p Fs(\021)s Fz(\))2525 385 y Fo(l)q FA(\000)p Fr(2+)2702 358 y Fi(4)p 2703 370 31 3 v 2703 411 a(2)2757 180 y Fp(!)2845 336 y Fq(j)-15 b(j)p Fs(Q)p Fq(j)g(j)2987 350 y FA(Q)3049 336 y Fq(j)g(j)p Fs(\032)3131 298 y FA(0)3155 336 y Fq(j)g(j)3190 298 y Fo(l)3190 358 y FA(C)3235 336 y Fq(j)g(j)p Fs(\020)7 b Fq(j)-15 b(j)3352 351 y FA(C)3393 332 y Fl(0)0 598 y Fz(and)30 b(so)778 751 y Fq(j)-15 b(j)p Fs(\032)860 766 y Fr(1)p Fo(;l)941 751 y Fq(j)g(j)976 765 y FA(C)1047 751 y Fq(\024)25 b Fs(n)1213 677 y Fp(\000)1254 713 y Fo(n)1254 773 y(n)p FA(\000)p Fr(1)1391 677 y Fp(\001)1458 689 y Fz(2)1503 656 y Fr(1)p Fo(=)p Fr(2)1613 689 y Fz(\()p Fs(S)1704 703 y Fr(6)1744 689 y Fs(C)1809 703 y Fr(6)1848 689 y Fz(\))1883 656 y Fr(3)1923 689 y Fs(K)2000 704 y Fo(l)p 1458 730 569 4 v 1692 813 a Fz(4)p Fs(\031)2036 751 y(C)2101 765 y Fo(R)2159 751 y Fz(\(4)p Fs(\031)s(C)2359 765 y FA(1)2435 751 y Fz(\))2470 713 y Fo(l)q FA(\000)p Fr(2)2586 751 y Fq(j)-15 b(j)p Fs(Q)p Fq(j)g(j)2728 765 y FA(Q)2790 751 y Fq(j)g(j)p Fs(\032)2872 713 y FA(0)2896 751 y Fq(j)g(j)2931 713 y Fo(l)2931 773 y FA(C)2977 751 y Fs(:)0 1022 y Fq(\017)61 b Fs(\032)153 1037 y Fr(0)p Fo(;l)266 1022 y Fy(with)34 b Fs(l)27 b Fq(\025)e Fz(5.)41 b(W)-8 b(e)32 b(w)m(an)m(t)f(to)g(estimate)83 1298 y Fq(j)118 1275 y Fp(c)108 1298 y Fs(Q)180 1313 y Fo(\020)220 1298 y Fz(\()p Fs(p;)15 b(p)p Fz(\))p Fq(j)26 b(\024)796 1237 y Fz(1)p 579 1277 480 4 v 579 1395 a(\(2)p Fs(\031)s Fz(\))749 1359 y Fr(1+)849 1326 y Fi(3\()p Fg(n)p Fi(+1\))p 850 1344 194 3 v 932 1385 a(2)1083 1174 y Fp(Z)1174 1201 y Fr(+)p FA(1)1134 1381 y(\0001)1319 1298 y Fs(d\021)1430 1174 y Fp(Z)1506 1298 y Fq(\001)15 b(\001)g(\001)1596 1174 y Fp(Z)1994 1237 y Fz(1)p 1712 1277 608 4 v 1712 1364 a(\()p Fs(E)5 b Fz(\()p Fs(p)p Fz(\))1935 1338 y Fr(2)1996 1364 y Fz(+)20 b Fs(\021)2135 1338 y Fr(2)2175 1364 y Fz(\))2210 1338 y Fr(1)p Fo(=)p Fr(4)2330 1298 y Fq(j)2372 1274 y Fp(b)2355 1298 y Fs(')2414 1272 y FA(0)2438 1298 y Fz(\()p Fs(p)h Fq(\000)f Fs(p)2677 1312 y Fr(1)2716 1298 y Fz(\))p Fq(j\002)335 1616 y(\002)737 1555 y Fz(1)p 436 1595 648 4 v 436 1683 a(\()p Fs(E)5 b Fz(\()p Fs(p)624 1697 y Fr(1)664 1683 y Fz(\))699 1656 y Fr(2)759 1683 y Fz(+)20 b Fs(\021)898 1656 y Fr(2)938 1683 y Fz(\))973 1656 y Fr(1)p Fo(=)p Fr(4)1108 1503 y Fo(n)p FA(\000)p Fr(1)1117 1530 y Fp(Y)1114 1725 y Fo(j)t Fr(=1)1256 1488 y Fp(\022)1633 1555 y Fz(1)p 1333 1595 645 4 v 1333 1683 a(\()p Fs(E)5 b Fz(\()p Fs(p)1521 1697 y Fo(j)1559 1683 y Fz(\))1594 1656 y Fr(2)1654 1683 y Fz(+)20 b Fs(\021)1793 1656 y Fr(2)1832 1683 y Fz(\))1867 1656 y Fr(1)p Fo(=)p Fr(4)1988 1616 y Fq(j)2029 1592 y Fp(b)2013 1616 y Fs(')2072 1590 y FA(0)2096 1616 y Fz(\()p Fs(p)2177 1630 y Fo(j)2234 1616 y Fq(\000)f Fs(p)2370 1630 y Fo(j)t Fr(+1)2497 1616 y Fz(\))p Fq(j)2912 1555 y Fz(1)p 2567 1595 735 4 v 2567 1683 a(\()p Fs(E)5 b Fz(\()p Fs(p)2755 1697 y Fo(j)t Fr(+1)2883 1683 y Fz(\))2918 1656 y Fr(2)2978 1683 y Fz(+)20 b Fs(\021)3117 1656 y Fr(2)3157 1683 y Fz(\))3192 1656 y Fr(1)p Fo(=)p Fr(4)3312 1488 y Fp(\023)3394 1616 y Fq(\002)1436 1901 y(\002)1842 1839 y Fz(1)p 1537 1880 655 4 v 1537 1967 a(\()p Fs(E)5 b Fz(\()p Fs(p)1725 1981 y Fo(n)1773 1967 y Fz(\))1808 1941 y Fr(2)1868 1967 y Fz(+)20 b Fs(\021)2007 1941 y Fr(2)2047 1967 y Fz(\))2082 1941 y Fr(1)p Fo(=)p Fr(4)2202 1901 y Fq(j)2233 1877 y Fp(b)2227 1901 y Fs(\020)7 b Fz(\()p Fs(p)2355 1915 y Fo(n)2422 1901 y Fq(\000)20 b Fs(p)p Fz(\))p Fq(j)2911 1839 y Fz(1)p 2629 1880 608 4 v 2629 1967 a(\()p Fs(E)5 b Fz(\()p Fs(p)p Fz(\))2852 1941 y Fr(2)2913 1967 y Fz(+)20 b Fs(\021)3052 1941 y Fr(2)3092 1967 y Fz(\))3127 1941 y Fr(1)p Fo(=)p Fr(4)3262 1901 y Fs(dp)3355 1915 y Fr(1)3410 1901 y Fq(\001)15 b(\001)g(\001)h Fs(dp)3624 1915 y Fo(n)3671 1901 y Fs(:)0 2144 y Fz(Since)30 b(there)h(are)g(at)g(least)g(6)g(functions,)f(w)m(e) h(ma)m(y)g(use)f(\(48\))i(t)m(wice)g(and)e(obtain)658 2389 y Fq(jh)p Fs(\032)765 2352 y FA(0)765 2413 y Fr(0)p Fo(;l)846 2389 y Fs(;)15 b(\020)7 b Fq(i)q(j)25 b(\024)g Fs(n)1180 2328 y Fz(\()p Fs(S)1271 2342 y Fr(6)1310 2328 y Fs(C)1375 2342 y Fr(6)1415 2328 y Fz(\))1450 2295 y Fr(6)p 1180 2369 310 4 v 1284 2452 a Fz(4)p Fs(\031)1499 2389 y Fz(\(4)p Fs(\031)s(C)1699 2403 y FA(1)1775 2389 y Fz(\))1810 2352 y Fo(l)q FA(\000)p Fr(5)1942 2261 y Fp(\022)2046 2328 y Fz(1)p 2018 2369 101 4 v 2018 2452 a(2)p Fs(\031)2144 2266 y Fp(Z)2235 2292 y FA(1)2195 2472 y(\0001)2455 2328 y Fs(d\021)p 2349 2369 308 4 v 2349 2452 a(E)5 b Fz(\()p Fs(\021)s Fz(\))2539 2426 y Fo(l)q FA(\000)p Fr(2)2667 2261 y Fp(\023)2749 2389 y Fq(j)-15 b(j)p Fs(\032)2831 2352 y FA(0)2855 2389 y Fq(j)g(j)2890 2352 y Fo(n)2890 2412 y FA(C)2937 2389 y Fq(j)g(j)p Fs(\020)7 b Fq(j)-15 b(j)3054 2405 y FA(C)3095 2386 y Fl(0)0 2628 y Fz(and)30 b(so)1098 2773 y Fq(j)-15 b(j)p Fs(\032)1180 2788 y Fr(0)p Fo(;l)1262 2773 y Fq(j)g(j)1297 2787 y FA(C)1367 2773 y Fq(\024)25 b Fs(n)1528 2712 y Fz(\()p Fs(S)1619 2726 y Fr(6)1658 2712 y Fs(C)1723 2726 y Fr(6)1763 2712 y Fz(\))1798 2679 y Fr(6)p 1528 2752 310 4 v 1632 2836 a Fz(4)p Fs(\031)1847 2773 y Fz(\(4)p Fs(\031)s(C)2047 2787 y FA(1)2123 2773 y Fz(\))2158 2736 y Fo(l)q FA(\000)p Fr(5)2275 2773 y Fs(K)2352 2788 y Fo(l)q FA(\000)p Fr(2)2468 2773 y Fq(j)-15 b(j)p Fs(\032)2550 2736 y FA(0)2574 2773 y Fq(j)g(j)2609 2736 y Fo(n)2609 2796 y FA(C)2656 2773 y Fs(:)141 2954 y Fz(No)m(w)31 b(since)g Fs(K)648 2968 y Fo(n)p FA(\000)p Fr(2)811 2954 y Fq(\024)24 b Fs(K)983 2973 y Fr(\()p Fo(n)p Fr(+1\))p Fo(=)p Fr(2)1277 2954 y Fz(when)29 b Fs(n)c Fq(\025)g Fz(5,)31 b(w)m(e)g(obtain)990 3182 y Fq(j)-15 b(j)p Fs(\032)1072 3196 y Fo(n)1119 3182 y Fq(j)g(j)1154 3196 y FA(C)1225 3182 y Fq(\024)25 b Fs(nK)1463 3183 y Fg(n)p Fi(+1)p 1463 3196 116 3 v 1505 3237 a(2)1592 3182 y Fs(C)1657 3196 y Fo(\032)1712 3081 y Fp(\020)1767 3182 y Fs(C)1832 3196 y Fo(R)1889 3102 y Fq(p)p 1965 3102 46 4 v 80 x Fz(2)q Fq(j)-15 b(j)p Fs(Q)p Fq(j)g(j)2153 3196 y FA(Q)2235 3182 y Fz(+)20 b(2)2371 3112 y Fq(p)p 2447 3112 56 4 v 70 x Fs(\031)s Fq(j)-15 b(j)p Fs(\032)2584 3144 y FA(0)2608 3182 y Fq(j)g(j)2643 3196 y FA(C)2688 3081 y Fp(\021)2743 3104 y Fo(n)3618 3182 y Fz(\(50\))0 3390 y(with)624 3557 y Fs(C)689 3571 y Fo(\032)755 3557 y Fz(:=)886 3496 y Fs(S)942 3510 y Fr(6)981 3496 y Fs(C)1046 3510 y Fr(6)p 886 3536 200 4 v 936 3620 a Fz(4)p Fs(\031)1111 3557 y Fz(max)1295 3402 y Fp( )1367 3557 y Fz(1)p Fs(;)1452 3429 y Fp(\022)1530 3496 y Fs(C)1595 3510 y Fr(6)1634 3496 y Fs(S)1690 3510 y Fr(6)p 1530 3536 V 1541 3620 a Fz(2)1586 3555 y Fq(p)p 1663 3555 56 4 v 1663 3620 a Fs(\031)1739 3429 y Fp(\023)1806 3452 y Fr(2)1861 3557 y Fs(;)1901 3429 y Fp(\022)1978 3496 y Fs(C)2043 3510 y Fr(6)2083 3496 y Fs(S)2139 3510 y Fr(6)p 1978 3536 200 4 v 1990 3620 a Fz(2)2035 3555 y Fq(p)p 2111 3555 56 4 v 65 x Fs(\031)2188 3429 y Fp(\023)2255 3452 y Fr(5)2294 3402 y Fp(!)2391 3557 y Fz(=)2497 3496 y Fs(S)2553 3510 y Fr(6)2592 3496 y Fs(C)2657 3510 y Fr(6)p 2497 3536 200 4 v 2547 3620 a Fz(4)p Fs(\031)2722 3429 y Fp(\022)2799 3496 y Fs(C)2864 3510 y Fr(6)2903 3496 y Fs(S)2959 3510 y Fr(6)p 2799 3536 V 2810 3620 a Fz(2)2855 3555 y Fq(p)p 2932 3555 56 4 v 2932 3620 a Fs(\031)3008 3429 y Fp(\023)3075 3452 y Fr(5)3130 3557 y Fs(:)141 3789 y Fz(F)-8 b(or)33 b Fs(\032)353 3803 y Fr(4)392 3789 y Fz(,)f(w)m(e)h(notice)g(that)f Fs(\032)1099 3803 y Fr(0)p Fo(;)p Fr(4)1221 3789 y Fz(=)c(0)k(for)f(the)h(same)h (reason)f(as)g Fs(\032)2370 3803 y Fr(0)p Fo(;)p Fr(2)2464 3789 y Fz(,)g(and)g(that)g Fs(K)2975 3803 y Fr(2)3042 3789 y Fq(\025)c Fs(K)3218 3808 y Fr(5)p Fo(=)p Fr(2)3328 3789 y Fz(.)45 b(Therefore)0 3902 y(w)m(e)31 b(obtain)1116 4032 y Fq(j)-15 b(j)p Fs(\032)1198 4046 y Fr(4)1237 4032 y Fq(j)g(j)1272 4046 y FA(C)1343 4032 y Fq(\024)25 b Fs(C)1504 4046 y Fo(\032)1540 4055 y Fi(4)1594 3931 y Fp(\020)1648 4032 y Fs(C)1713 4046 y Fo(R)1771 3952 y Fq(p)p 1847 3952 46 4 v 80 x Fz(2)p Fq(j)-15 b(j)p Fs(Q)p Fq(j)g(j)2034 4046 y FA(Q)2117 4032 y Fz(+)20 b(2)2253 3962 y Fq(p)p 2329 3962 56 4 v 70 x Fs(\031)s Fq(j)-15 b(j)p Fs(\032)2466 3994 y FA(0)2490 4032 y Fq(j)g(j)2525 4046 y FA(C)2570 3931 y Fp(\021)2624 3953 y Fr(4)3618 4032 y Fz(\(51\))0 4209 y(with)611 4377 y Fs(C)676 4391 y Fo(\032)712 4400 y Fi(4)776 4377 y Fz(:=)907 4315 y(4)p Fs(K)1029 4329 y Fr(2)1069 4315 y Fs(S)1125 4329 y Fr(6)1165 4315 y Fs(C)1230 4329 y Fr(6)p 907 4356 362 4 v 1038 4439 a Fz(4)p Fs(\031)1294 4377 y Fz(max)1479 4221 y Fp( )1550 4377 y Fz(1)p Fs(;)1635 4248 y Fp(\022)1713 4315 y Fs(C)1778 4329 y Fr(6)1818 4315 y Fs(S)1874 4329 y Fr(6)p 1713 4356 200 4 v 1725 4439 a Fz(2)1770 4374 y Fq(p)p 1846 4374 56 4 v 65 x Fs(\031)1923 4248 y Fp(\023)1990 4271 y Fr(2)2029 4221 y Fp(!)2126 4377 y Fz(=)2232 4315 y Fs(S)2288 4329 y Fr(6)2327 4315 y Fs(C)2392 4329 y Fr(6)2432 4315 y Fs(K)2509 4329 y Fr(2)p 2232 4356 317 4 v 2363 4439 a Fs(\031)2574 4248 y Fp(\022)2651 4315 y Fs(C)2716 4329 y Fr(6)2755 4315 y Fs(S)2811 4329 y Fr(6)p 2651 4356 200 4 v 2662 4439 a Fz(2)2707 4374 y Fq(p)p 2783 4374 56 4 v 65 x Fs(\031)2860 4248 y Fp(\023)2927 4271 y Fr(2)2982 4377 y Fs(:)p 3102 4377 4 62 v 3106 4319 55 4 v 3106 4377 V 3160 4377 4 62 v 0 4687 a Fe(4.3.4)105 b(The)35 b(third)g(order)g(densit)m(y)g Fs(\032)1485 4701 y Fr(3)0 4858 y Fe(Lemma)g(14.)42 b Fy(We)32 b(have)1116 4988 y Fq(j)-15 b(j)p Fs(\032)1198 5002 y Fr(3)1237 4988 y Fq(j)g(j)1272 5002 y FA(C)1343 4988 y Fq(\024)25 b Fs(C)1504 5002 y Fo(\032)1540 5011 y Fi(3)1594 4887 y Fp(\020)1648 4988 y Fs(C)1713 5002 y Fo(R)1771 4908 y Fq(p)p 1847 4908 46 4 v 80 x Fz(2)p Fq(j)-15 b(j)p Fs(Q)p Fq(j)g(j)2034 5002 y FA(Q)2117 4988 y Fz(+)20 b(2)2253 4918 y Fq(p)p 2329 4918 56 4 v 70 x Fs(\031)s Fq(j)-15 b(j)p Fs(\032)2466 4950 y FA(0)2490 4988 y Fq(j)g(j)2525 5002 y FA(C)2570 4887 y Fp(\021)2624 4909 y Fr(3)0 5165 y Fy(and)34 b(ther)-5 b(efor)g(e)1394 5278 y Fq(j)-15 b(j)p Fz(\()p Fs(Q)1536 5292 y Fr(3)1576 5278 y Fs(;)15 b(\032)1663 5292 y Fr(3)1703 5278 y Fz(\))p Fq(j)-15 b(j)26 b(\024)f Fs(\024)1947 5292 y Fr(3)2002 5201 y Fp(\014)2002 5255 y(\014)2017 5201 y(\014)2017 5255 y(\014)2047 5278 y Fz(\()p Fs(Q;)15 b(\032)2241 5241 y FA(0)2265 5278 y Fz(\))2300 5201 y Fp(\014)2300 5255 y(\014)2316 5201 y(\014)2316 5255 y(\014)2346 5227 y Fr(3)0 5438 y Fy(with)600 5584 y Fs(\024)652 5598 y Fr(3)717 5584 y Fz(=)25 b(3)p Fs(C)923 5598 y Fo(R)982 5584 y Fs(K)1059 5603 y Fr(3)p Fo(=)p Fr(2)1169 5584 y Fs(C)1234 5598 y Fo(Q)1293 5505 y Fq(p)p 1369 5505 46 4 v 79 x Fz(2)c(+)f(2)1571 5514 y Fq(p)p 1647 5514 56 4 v 70 x Fs(\031)s(C)1767 5598 y Fo(\032)1803 5607 y Fi(3)1842 5584 y Fs(;)201 b(C)2133 5598 y Fo(\032)2169 5607 y Fi(3)2233 5584 y Fz(=)2339 5522 y(15)p Fs(C)2494 5536 y Fo(M)2574 5522 y Fs(S)2630 5536 y Fr(6)2669 5522 y Fz(\()p Fs(S)2760 5536 y Fr(6)p Fo(;)p Fr(4)2855 5522 y Fz(\))2890 5489 y Fr(2)2929 5522 y Fz(\()p Fs(C)3029 5536 y Fr(6)3069 5522 y Fz(\))3104 5489 y Fr(4)p 2339 5563 805 4 v 2539 5647 a Fs(\031)s Fz(\(4)p Fs(\031)s(C)2794 5661 y FA(1)2869 5647 y Fz(\))2904 5620 y Fr(3)3154 5584 y Fs(:)1844 5906 y Fz(32)p eop end %%Page: 33 33 TeXDict begin 33 32 bop 0 63 a Fy(Pr)-5 b(o)g(of)34 b({)63 b Fz(Notice)32 b(that)f(thanks)f(to)h(the)g(previous)f(pro)s(of,)f(w)m (e)i(already)g(ha)m(v)m(e)h(some)e(estimates)i(on)e Fs(\032)3488 77 y Fr(3)p Fo(;)p Fr(0)3583 63 y Fz(,)g Fs(\032)3685 77 y Fr(2)p Fo(;)p Fr(1)0 176 y Fz(and)f Fs(\032)223 190 y Fr(1)p Fo(;)p Fr(2)318 176 y Fz(.)40 b(It)30 b(remains)g(to)g (study)f Fs(\032)1227 190 y Fr(0)p Fo(;)p Fr(3)1322 176 y Fz(.)40 b(As)30 b(b)s(efore)g(and)f(as)h(in)g([16)q(],)g(w)m(e)g(ha)m (v)m(e)i(to)e(compute)g Fs(\032)3251 190 y Fr(0)p Fo(;)p Fr(3)3375 176 y Fz(explicitely)0 289 y(b)m(y)g(a)h(residuum)e(form)m (ula.)41 b(W)-8 b(e)31 b(th)m(us)f(write)1401 459 y Fs(\032)1448 473 y Fr(0)p Fo(;)p Fr(3)1567 459 y Fz(=)1796 372 y Fp(X)1663 574 y Fo(\017)1692 583 y Fi(1)1726 574 y Fo(;:::;\017)1855 583 y Fi(4)1888 574 y FA(2f\006g)2075 459 y Fs(\032)2122 418 y Fo(\017)2151 427 y Fi(1)2185 418 y Fo(\017)2214 427 y Fi(2)2248 418 y Fo(\017)2277 427 y Fi(3)2312 418 y Fo(\017)2341 427 y Fi(4)2122 485 y Fr(0)p Fo(;)p Fr(3)0 719 y Fz(with)g(an)g(ob)m(vious)h(de\014nition.)0 903 y Fq(\017)g Fz(Let)g(us)e(treat)j(\014rst)d Fs(\032)812 865 y Fr(+)p FA(\000\000\000)812 929 y Fr(0)p Fo(;)p Fr(3)1036 903 y Fz(.)41 b(W)-8 b(e)31 b(th)m(us)f(\014x)g(some)h Fs(\020)h Fq(2)24 b(C)2025 870 y FA(0)2069 903 y Fq(\\)c Fs(L)2212 870 y Fr(2)2282 903 y Fz(and)29 b(estimate)j(the)f(term)93 1152 y Fp(c)83 1175 y Fs(Q)155 1190 y Fo(\020)195 1175 y Fz(\()p Fs(p;)15 b(p)p Fz(\))25 b(=)g(\(2)p Fs(\031)s Fz(\))688 1138 y FA(\000)p Fr(6)799 1051 y Fp(Z)10 b(Z)f(Z)1026 1175 y Fs(dp)1119 1189 y Fr(1)1174 1175 y Fs(dp)1267 1189 y Fr(2)1322 1175 y Fs(dp)1415 1189 y Fr(3)1464 1114 y Fz(\003)1527 1081 y Fr(+)1586 1114 y Fz(\()p Fs(p)p Fz(\))1719 1090 y Fp(b)1702 1114 y Fs(')1761 1087 y FA(0)1786 1114 y Fz(\()p Fs(p)20 b Fq(\000)g Fs(p)2024 1128 y Fr(1)2063 1114 y Fz(\)\003)2161 1081 y FA(\000)2220 1114 y Fz(\()p Fs(p)2301 1128 y Fr(1)2341 1114 y Fz(\))p 1464 1154 913 4 v 1656 1238 a Fs(E)5 b Fz(\()p Fs(p)p Fz(\))21 b(+)f Fs(E)5 b Fz(\()p Fs(p)2109 1252 y Fr(1)2149 1238 y Fz(\))2386 1175 y Fq(\002)1775 1445 y(\002)1892 1359 y Fp(b)1876 1383 y Fs(')1935 1357 y FA(0)1959 1383 y Fz(\()p Fs(p)2040 1397 y Fr(1)2100 1383 y Fq(\000)20 b Fs(p)2237 1397 y Fr(2)2276 1383 y Fz(\)\003)2374 1350 y FA(\000)2433 1383 y Fz(\()p Fs(p)2514 1397 y Fr(2)2554 1383 y Fz(\))2605 1359 y Fp(b)2589 1383 y Fs(')2648 1357 y FA(0)2672 1383 y Fz(\()p Fs(p)2753 1397 y Fr(2)2813 1383 y Fq(\000)f Fs(p)2949 1397 y Fr(3)2989 1383 y Fz(\)\003)3087 1350 y FA(\000)3146 1383 y Fz(\()p Fs(p)3227 1397 y Fr(3)3267 1383 y Fz(\))p 1876 1424 1426 4 v 1990 1507 a(\()p Fs(E)5 b Fz(\()p Fs(p)p Fz(\))22 b(+)e Fs(E)5 b Fz(\()p Fs(p)2479 1521 y Fr(2)2518 1507 y Fz(\)\)\()p Fs(E)g Fz(\()p Fs(p)p Fz(\))22 b(+)e Fs(E)5 b Fz(\()p Fs(p)3077 1521 y Fr(3)3117 1507 y Fz(\)\))3318 1421 y Fp(b)3312 1445 y Fs(\020)i Fz(\()p Fs(p)3440 1459 y Fr(3)3499 1445 y Fq(\000)20 b Fs(p)p Fz(\))p Fs(;)0 1650 y Fz(b)m(y)83 1948 y Fq(j)118 1925 y Fp(c)108 1948 y Fs(Q)180 1963 y Fo(\020)220 1948 y Fz(\()p Fs(p;)15 b(p)p Fz(\))p Fq(j)26 b(\024)f Fz(\(2)p Fs(\031)s Fz(\))739 1911 y FA(\000)p Fr(6)850 1824 y Fp(Z)9 b(Z)h(Z)1077 1948 y Fs(dp)1170 1962 y Fr(1)1225 1948 y Fs(dp)1318 1962 y Fr(2)1372 1948 y Fs(dp)1465 1962 y Fr(3)1515 1749 y Fp(\014)1515 1804 y(\014)1515 1858 y(\014)1545 1854 y Fz(\003)1608 1821 y Fr(+)1667 1854 y Fz(\()p Fs(p)p Fz(\))1800 1830 y Fp(b)1783 1854 y Fs(')1842 1827 y FA(0)1866 1854 y Fz(\()p Fs(p)21 b Fq(\000)f Fs(p)2105 1868 y Fr(1)2144 1854 y Fz(\)\003)2242 1821 y FA(\000)2301 1854 y Fz(\()p Fs(p)2382 1868 y Fr(1)2422 1854 y Fz(\))2457 1749 y Fp(\014)2457 1804 y(\014)2457 1858 y(\014)p 1515 1927 973 4 v 1753 2014 a Fs(E)5 b Fz(\()p Fs(p)21 b Fz(+)f Fs(p)2064 2028 y Fr(1)2103 2014 y Fz(\))2138 1988 y Fr(2)p Fo(=)p Fr(3)2497 1948 y Fq(\002)2104 2269 y(\002)2205 2070 y Fp(\014)2205 2125 y(\014)2205 2179 y(\014)2251 2151 y(b)2235 2175 y Fs(')2294 2149 y FA(0)2318 2175 y Fz(\()p Fs(p)2399 2189 y Fr(1)2459 2175 y Fq(\000)g Fs(p)2596 2189 y Fr(2)2635 2175 y Fz(\))2670 2070 y Fp(\014)2670 2125 y(\014)2670 2179 y(\014)2716 2070 y(\014)2716 2125 y(\014)2716 2179 y(\014)2762 2151 y(b)2746 2175 y Fs(')2805 2149 y FA(0)2829 2175 y Fz(\()p Fs(p)2910 2189 y Fr(2)2969 2175 y Fq(\000)g Fs(p)3106 2189 y Fr(3)3146 2175 y Fz(\))3181 2070 y Fp(\014)3181 2125 y(\014)3181 2179 y(\014)p 2205 2248 1007 4 v 2330 2336 a Fs(E)5 b Fz(\()p Fs(p)2483 2350 y Fr(1)2523 2336 y Fz(\))2558 2309 y Fr(1)p Fo(=)p Fr(3)2669 2336 y Fs(E)g Fz(\()p Fs(p)2822 2350 y Fr(2)2862 2336 y Fz(\))p Fs(E)g Fz(\()p Fs(p)p Fz(\))3236 2165 y Fp(\014)3236 2219 y(\014)3236 2274 y(\014)3272 2245 y(b)3267 2269 y Fs(\020)h Fz(\()p Fs(p)3394 2283 y Fr(3)3454 2269 y Fq(\000)20 b Fs(p)p Fz(\))3626 2165 y Fp(\014)3626 2219 y(\014)3626 2274 y(\014)3671 2269 y Fs(:)0 2478 y Fz(So)30 b(if)h(w)m(e)f(follo)m(w)i (the)f(metho)s(d)e(used)h(ab)s(o)m(v)m(e,)i(w)m(e)f(obtain)1141 2690 y Fq(j)-15 b(j)p Fs(\032)1223 2652 y Fr(+)p FA(\000\000\000)1223 2716 y Fr(0)p Fo(;)p Fr(3)1447 2690 y Fq(j)g(j)1482 2704 y FA(C)1552 2690 y Fq(\024)1658 2628 y Fz(3)p Fs(C)1768 2642 y Fo(M)1848 2628 y Fs(S)1904 2642 y Fr(6)1943 2628 y Fz(\()p Fs(S)2034 2642 y Fr(6)p Fo(;)p Fr(4)2128 2628 y Fz(\))2163 2595 y Fr(2)2203 2628 y Fz(\()p Fs(C)2303 2642 y Fr(6)2343 2628 y Fz(\))2378 2595 y Fr(4)p 1658 2670 760 4 v 1988 2753 a Fz(4)p Fs(\031)2428 2690 y Fq(j)g(j)p Fs(\032)2510 2653 y FA(0)2533 2690 y Fq(j)g(j)2568 2653 y Fr(3)2568 2713 y FA(C)2614 2690 y Fs(:)141 2888 y Fz(No)m(w,)34 b(it)f(is)g(easily)g(seen)g(that)g Fs(\032)1261 2850 y FA(\000)p Fr(+++)1261 2914 y(0)p Fo(;)p Fr(3)1484 2888 y Fz(,)h Fs(\032)1590 2850 y FA(\000\000\000)p Fr(+)1590 2914 y(0)p Fo(;)p Fr(3)1813 2888 y Fz(,)g 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y Fz(\))15 b Fq(\001)g(\001)g(\001)i Fs(a)1671 1556 y FA(\003)1671 1616 y Fo(P)1730 1593 y Fz(\()p Fs(f)1810 1607 y Fo(n)1857 1593 y Fz(\))e Fs(b)1946 1556 y FA(\003)1946 1616 y Fo(P)2005 1593 y Fz(\()p Fs(g)2083 1607 y Fr(1)2123 1593 y Fz(\))g Fq(\001)g(\001)g(\001)i Fs(b)2334 1556 y FA(\003)2334 1616 y Fo(P)2392 1593 y Fz(\()p Fs(g)2470 1607 y Fo(m)2538 1593 y Fz(\))e(\012)2654 1607 y Fo(P)2713 1593 y Fs(;)0 1793 y Fz(where)35 b(\()p Fs(f)348 1807 y Fr(1)387 1793 y Fs(;)15 b(:::;)g(f)587 1807 y Fo(n)635 1793 y Fz(\))33 b Fq(2)g Fz(\()p Fq(H)910 1760 y Fo(P)909 1816 y Fr(+)969 1793 y Fz(\))1004 1760 y Fo(n)1086 1793 y Fz(and)h(\()p Fs(g)1345 1807 y Fr(1)1385 1793 y Fs(;)15 b(:::;)g(g)1583 1807 y Fo(m)1652 1793 y Fz(\))33 b Fq(2)g Fz(\()p Fq(H)1927 1760 y Fo(P)1926 1816 y FA(\000)1986 1793 y Fz(\))2021 1760 y Fo(m)2122 1793 y Fz(are)j(suc)m(h)f(that)g Fq(h)p Fs(f)2770 1807 y Fo(i)2798 1793 y Fs(;)15 b(f)2883 1807 y Fo(j)2920 1793 y Fq(i)33 b Fz(=)g Fs(\016)3132 1807 y Fo(ij)3193 1793 y Fz(,)j Fq(h)p Fs(g)3332 1807 y Fo(i)3361 1793 y Fs(;)15 b(g)3444 1807 y Fo(j)3481 1793 y Fq(i)34 b Fz(=)e Fs(\016)3693 1807 y Fo(ij)3754 1793 y Fz(,)0 1906 y(and)j(\012)248 1920 y Fo(P)342 1906 y Fz(is)g(the)h(dressed)f(v)-5 b(acuum)35 b(in)g Fq(F)45 b Fz(obtained)36 b(b)m(y)f(Theorem)h(5.)56 b(The)36 b Fy(one-b)-5 b(o)g(dy)38 b(density)g(matrix)48 b Fz(of)0 2019 y(suc)m(h)30 b(a)h(state)h(is)e(the)h(op)s(erator)f Fs(\015)1165 2034 y Fo( )1248 2019 y Fz(de\014ned)f(b)m(y)i(its)f(k)m (ernel)1023 2293 y Fs(\015)1070 2308 y Fo( )1123 2293 y Fz(\()p Fs(x;)15 b(y)s Fz(\))26 b(=)1499 2180 y Fo(n)1455 2207 y Fp(X)1463 2402 y Fo(i)p Fr(=1)1601 2293 y Fs(f)1646 2307 y Fo(i)1674 2293 y Fz(\()p Fs(x)p Fz(\))p 1796 2214 192 4 v Fs(f)1841 2307 y Fo(i)1869 2293 y Fz(\()p Fs(y)s Fz(\))1988 2233 y Fo(T)2063 2293 y Fq(\000)2188 2180 y Fo(m)2154 2207 y Fp(X)2158 2402 y Fo(j)t Fr(=1)2301 2293 y Fs(g)2344 2307 y Fo(j)2380 2293 y Fz(\()p Fs(x)p Fz(\))p 2502 2214 199 4 v Fs(g)2545 2307 y Fo(j)2583 2293 y Fz(\()p Fs(y)s Fz(\))2701 2233 y Fo(T)0 2583 y Fz(often)31 b(written)f(as)1291 2742 y Fs(\015)1338 2757 y Fo( )1416 2742 y Fz(=)1556 2629 y Fo(n)1512 2656 y Fp(X)1520 2851 y Fo(i)p Fr(=1)1658 2742 y Fq(j)p Fs(f)1728 2756 y Fo(i)1756 2742 y Fq(ih)p Fs(f)1871 2756 y Fo(i)1900 2742 y Fq(j)20 b(\000)2070 2629 y Fo(m)2036 2656 y Fp(X)2040 2851 y Fo(j)t Fr(=1)2182 2742 y Fq(j)p Fs(g)2250 2756 y Fo(j)2288 2742 y Fq(ih)p Fs(g)2401 2756 y Fo(j)2438 2742 y Fq(j)p Fs(;)0 2997 y Fz(and)30 b(it)h(satis\014es)1526 3110 y Fq(\000)p Fs(P)38 b Fq(\024)25 b Fs(\015)1836 3125 y Fo( )1914 3110 y Fq(\024)g Fz(1)c Fq(\000)f Fs(P)s(:)0 3274 y Fz(The)30 b(asso)s(ciated)i Fy(density)h(of)g(char)-5 b(ge)38 b Fz(is)30 b(the)h(function)f Fs(\032)1978 3289 y Fo( )2031 3274 y Fz(\()p Fs(x)p Fz(\))c(=)f(T)-8 b(r)2368 3294 y Fj(C)2416 3275 y Fi(4)2470 3274 y Fz(\()q Fs(\015)5 b Fz(\()p Fs(x;)15 b(x)p Fz(\)\))31 b(or)1214 3548 y Fs(\032)1261 3563 y Fo( )1314 3548 y Fz(\()p Fs(x)p Fz(\))26 b(=)1602 3435 y Fo(n)1558 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Fz(\()p Fs(P)s(;)15 b(\015)755 4339 y Fo( )808 4324 y Fz(\))84 b(:=)f Fq(h)p Fs( )s Fq(j)p Fm(H)p Fq(j)p Fs( )s Fq(i)27 b Fz(=)e(tr)1630 4195 y Fp(\022\022)1764 4324 y Fs(D)1842 4286 y Fo(\013')1957 4324 y Fz(+)20 b Fs(\013\032)2153 4338 y Fo(Q)2233 4324 y Fq(\003)2344 4262 y Fz(1)p 2309 4303 117 4 v 2309 4386 a Fq(j)g(\001)h(j)2455 4324 y(\000)f Fs(\013)2614 4262 y(Q)p Fz(\()p Fs(x;)15 b(y)s Fz(\))p 2614 4303 283 4 v 2625 4386 a Fq(j)p Fs(x)21 b Fq(\000)f Fs(y)s Fq(j)2907 4195 y Fp(\023)2989 4324 y Fs(\015)3036 4339 y Fo( )3089 4195 y Fp(\023)1106 4582 y Fz(+)1187 4521 y Fs(\013)p 1187 4561 59 4 v 1194 4645 a Fz(2)1270 4458 y Fp(Z)9 b(Z)1447 4519 y Fs(\032)1494 4534 y Fo( )1546 4519 y Fz(\()p Fs(x)p Fz(\))p Fs(\032)1715 4534 y Fo( )1768 4519 y Fz(\()p Fs(y)s Fz(\))p 1447 4561 441 4 v 1536 4645 a Fq(j)p Fs(x)20 b Fq(\000)g Fs(y)s Fq(j)1897 4582 y Fs(dx)15 b(dy)24 b Fq(\000)2228 4521 y Fs(\013)p 2228 4561 59 4 v 2235 4645 a Fz(2)2311 4458 y Fp(Z)10 b(Z)2488 4519 y Fq(j)p Fs(\015)2560 4534 y Fo( )2613 4519 y Fz(\()p Fs(x;)15 b(y)s Fz(\))p Fq(j)2848 4486 y Fr(2)p 2488 4561 401 4 v 2557 4645 a Fq(j)p Fs(x)21 b Fq(\000)f Fs(y)s Fq(j)2898 4582 y Fs(dx)15 b(dy)24 b Fz(+)c Fq(E)8 b Fz(\()p Fs(Q)p Fz(\))939 4769 y(=)96 b Fq(E)8 b Fz(\()p Fs(Q)20 b Fz(+)g Fs(\015)1427 4784 y Fo( )1480 4769 y Fz(\))p Fs(:)0 5054 y Ft(References)45 5257 y Fz([1])47 b(J.)36 b(Avron,)h(R.)f(Seiler,)i(B.)e(Simon.)g(The)f (Index)g(of)h(a)h(P)m(air)f(of)g(Pro)5 b(jections.)37 b Fy(Journal)i(of)f(F)-7 b(unctional)187 5370 y(A)n(nalysis)p Fz(,)31 b(120:)42 b(220{237,)34 b(1994.)45 5556 y([2])47 b(V.)38 b(Bac)m(h,)k(J.-M.)d(Barbaroux,)h(B.)f(Hel\013er,)i(H.)e (Sieden)m(top.)g(On)e(the)h(Stabilit)m(y)i(of)e(the)h(Relativistic)187 5669 y(Electron-P)m(ositron)32 b(Field.)f Fy(Commun.)j(Math.)f(Phys.)p Fz(,)e(201:)42 b(445{460,)34 b(1999.)1844 5906 y(37)p eop end %%Page: 38 38 TeXDict begin 38 37 bop 45 68 a Fz([3])47 b(V.)26 b(Bac)m(h,)j(E.H.)e (Lieb,)g(J.P)-8 b(.)27 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