The distribution of spacings between quadratic residues

1998/12/08 by P. Kurlberg, Kurlberg, P., Z. Rudnick +1
Mathematics · Physics and Astronomy · #11 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Number Theory (math.NT) #math-ph #math.MP #math.NT #msc:11

paper · pdf · doi:10.48550/arxiv.math/9812046

38 pages; introduction and section 6.2 revised, references updated. To appear in Duke Math. Journal

arxiv created 1999/01/07 · arxiv updated 2009/11/30

Abstract

We study the distribution of spacings between squares modulo q, where q is square-free and highly composite, in the limit as the number of prime factors of q goes to infinity. We show that all correlation functions are Poissonian, which among other things, implies that the spacings between nearest neighbors, normalized to have unit mean, have an exponential distribution.

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