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Square-full polynomials in short intervals and in arithmetic progressions

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  • E. Roditty-Gershon
Original languageEnglish
Article number3
Number of pages18
JournalResearch in Number Theory
Volume3
DOIs
DateAccepted/In press - 23 Nov 2016
DatePublished (current) - 17 Jan 2017

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] 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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    Rights statement: This is the final published version of the article (version of record). It first appeared online via Springer at https://doi.org/10.1007/s40993-016-0066-2 . Please refer to any applicable terms of use of the publisher.

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