- 99-348 Jens Marklof
- The n-point correlations between values of a linear form
(with an appendix by Zeev Rudnick)
(280K, gzipped postscript)
Sep 21, 99
(auto. generated ps),
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Abstract. We show that the n-point correlation function for the fractional
parts of a random linear form in m variables has a limit distribution
with power-like tail. The existence of the limit distribution
follows from the mixing property of flows on SL(m+1,R)/SL(m+1,Z).
Moreover, we prove similar limit theorems (i) for the probability
to find the fractional part of a random linear form close to zero,
and (ii) also for related trigonometric sums. For large $m$ all of
the above limit distributions approach the classical distributions
for independent uniformly distributed random variables.