2:00 pm Thursday, October 6, 2005
Number Theory Seminar: Mahler Measure and Weil Height in non-Abelian Extensions of the Rationals by J. Garza (UT Austin) in RLM 12.166
In a 1998 paper, Francesco Amoroso and Roberto Dvornicich, produced an absolute lower bound for the height of the algebraic numbers (different from zero and the roots of unity) lying in abelian extensions of the rationals. Motivated by this paper, I have set out to investigate the possibility of producing an absolute lower bound for the height or Mahler measure of algebraic numbers (different from zero and the roots of unity) that are not in abelian extensions of the rationals. In particular, the following question has been asked. Given an isomorphism class of finite groups, can a lower bound for the Mahler measure or Weil height be found for elements (different form zero and the roots of unity) in Galois extenions of the rationals having Galios group in the isomorphism class? Here, I will present three theorems that I have recently proved in this direction and will discuss some important considerations for further investigation. (candidacy talk) Submitted by
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