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1 April 2021 Square-root cancellation for sums of factorization functions over short intervals in function fields
Will Sawin
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Duke Math. J. 170(5): 997-1026 (1 April 2021). DOI: 10.1215/00127094-2020-0060

Abstract

We present new estimates for sums of the divisor function and other similar arithmetic functions in short intervals over function fields. (When the intervals are long, one obtains a good estimate from the Riemann hypothesis.) We obtain an estimate that approaches square-root cancellation as long as the characteristic of the finite field is relatively large. This is done by a geometric method, inspired by work of Hast and Matei, where we calculate the singular locus of a variety whose Fq-points control this sum. This has applications to highly unbalanced moments of L-functions.

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Will Sawin. "Square-root cancellation for sums of factorization functions over short intervals in function fields." Duke Math. J. 170 (5) 997 - 1026, 1 April 2021. https://doi.org/10.1215/00127094-2020-0060

Information

Received: 10 February 2019; Revised: 12 August 2020; Published: 1 April 2021
First available in Project Euclid: 18 March 2021

Digital Object Identifier: 10.1215/00127094-2020-0060

Subjects:
Primary: 11T55
Secondary: 11M38

Rights: Copyright © 2021 Duke University Press

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Vol.170 • No. 5 • 1 April 2021
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