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
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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.

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