ID: math/9812046

The distribution of spacings between quadratic residues

December 8, 1998

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P. Kurlberg, Z. Rudnick
Mathematics
Number Theory
Mathematical Physics

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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