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arXiv · 1110.0078

The distribution of the maximum of character sums

Jonathan Bober·Leo Goldmakher
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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.

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Jonathan Bober, Leo Goldmakher. 2012-04-16. The distribution of the maximum of character sums. https://doi.org/10.1112/s002557931200109x

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