The distribution of the maximum of character sums

We obtain explicit bounds on the moments of character sums, refining estimates of Montgomery and Vaughan. As an application we obtain results on the distribution of the maximal magnitude of character sums normalized by the square root of the modulus, finding almost double exponential decay in the ta...

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Bibliographic Details
Published in:arXiv.org 2012-04
Main Authors: Bober, Jonathan, Goldmakher, Leo
Format: Article
Language:English
Subjects:
Sums
Online Access:Get full text
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Summary:We obtain explicit bounds on the moments of character sums, refining estimates of Montgomery and Vaughan. As an application we obtain results on the distribution of the maximal magnitude of character sums normalized by the square root of the modulus, finding almost double exponential decay in the tail of this distribution.
ISSN:2331-8422
DOI:10.48550/arxiv.1110.0078