English

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 Fq[T]F_{q}[T] of polynomials over a finite field FqF_{q} of qq elements, in the limit qq\rightarrow\infty. 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.

Keywords

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}
}
R2 v1 2026-06-22T13:56:08.341Z