The distribution of spacings between quadratic residues
Number Theory
2007-05-23 v2 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.math/9812046,
title = {The distribution of spacings between quadratic residues},
author = {P. Kurlberg and Z. Rudnick},
journal= {arXiv preprint arXiv:math/9812046},
year = {2007}
}
Comments
38 pages; introduction and section 6.2 revised, references updated. To appear in Duke Math. Journal