The distribution of the maximum of character sums
Number Theory
2014-01-14 v2
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.
Keywords
Cite
@article{arxiv.1110.0078,
title = {The distribution of the maximum of character sums},
author = {Jonathan Bober and Leo Goldmakher},
journal= {arXiv preprint arXiv:1110.0078},
year = {2014}
}
Comments
16 pages, 1 figure, new version with corrections