Poisson spacing statistics for value sets of polynomials
Number Theory
2007-05-23 v1
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.
Cite
@article{arxiv.math/0602673,
title = {Poisson spacing statistics for value sets of polynomials},
author = {P. Kurlberg},
journal= {arXiv preprint arXiv:math/0602673},
year = {2007}
}
Comments
25 pages