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Poisson spacing statistics for value sets of polynomials

P. Kurlberg
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Abstract

If f is a polynomial with integer coefficients and q is an integer, we may regard f as a map from Z/qZ to Z/qZ. We show that the distribution of the (normalized) spacings between consecutive elements in the image of these maps becomes Poissonian as q tends to infinity along any sequence of square free integers such that the mean spacing modulo q tends to infinity.

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P. Kurlberg. 2006-02-28. Poisson spacing statistics for value sets of polynomials. https://arxiv.org/abs/math/0602673

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