Square-full polynomials in short intervals and in arithmetic progressions

E. Roditty-Gershon

doi:10.1007/s40993-016-0066-2

Square-full polynomials in short intervals and in arithmetic progressions

E. Roditty-Gershon^*

^*Corresponding author for this work

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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→ ∞. 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.

Original language	English
Article number	3
Number of pages	18
Journal	Research in Number Theory
Volume	3
DOIs	https://doi.org/10.1007/s40993-016-0066-2
Publication status	Published - 17 Jan 2017

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AB - 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] of polynomials over a finite field Fq of q elements, in the limit q→ ∞. 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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Square-full polynomials in short intervals and in arithmetic progressions

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