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THE DISTRIBUTION OF THE MAXIMUM OF CHARACTER SUMS

Part of: Exponential sums and character sums

Published online by Cambridge University Press:  08 January 2013

Jonathan W. Bober  and
Leo Goldmakher
Jonathan W. Bober
Affiliation:
Department of Mathematics, University of Washington, Seattle, WA, U.S.A. (email: jwbober@math.washington.edu)
Leo Goldmakher
Affiliation:
Department of Mathematics, University of Toronto, Toronto, ON, Canada (email: leo.goldmakher@utoronto.ca)
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Abstract

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.

MSC classification

Secondary: 11L40: Estimates on character sums
Type
Research Article
Information
Mathematika , Volume 59 , Issue 2 , July 2013 , pp. 427 - 442
Copyright
Copyright © 2013 University College London 

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