Lower bounds on odd order character sums

2011/09/07 by Goldmakher, Leo, Lamzouri, Youness
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1109.1348

Abstract

A classical result of Paley shows that there are infinitely many quadratic characters χ\modq whose character sums get as large as √(q)log log q; this implies that a conditional upper bound of Montgomery and Vaughan cannot be improved. In this paper, we derive analogous lower bounds on character sums for characters of odd order, which are best possible in view of the corresponding conditional upper bounds recently obtained by the first author.

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