Square-full polynomials in short intervals and in arithmetic progressions
Number Theory
2016-05-10 v1
Abstract
We study the variance of sums of the indicator function of square-full polynomials in both arithmetic progressions and short intervals. Our work is in the context of the ring of polynomials over a finite field of elements, in the limit . We use a recent equidistribution result due to N. Katz to express these variances in terms of triple matrix integrals over the unitary group, and evaluate them.
Cite
@article{arxiv.1605.02478,
title = {Square-full polynomials in short intervals and in arithmetic progressions},
author = {Edva Roditty-Gershon},
journal= {arXiv preprint arXiv:1605.02478},
year = {2016}
}