Square-full polynomials in short intervals and in arithmetic progressions

Edva Roditty-Gershon

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arXiv · 1605.02478

Square-full polynomials in short intervals and in arithmetic progressions

Edva Roditty-Gershon

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

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Edva Roditty-Gershon. 2016-05-09. Square-full polynomials in short intervals and in arithmetic progressions. https://arxiv.org/abs/1605.02478

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