The distribution of spacings between quadratic residues

Details The distribution of spacings between quadratic residues The distribution of spacings between quadratic residues

1998-12-08

arxiv.org/abs/math/9812046v2

Mathematics

Number Theory

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

Scientific paper

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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