Long large character sums

Crystel Bujold

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arXiv · 2005.11386

Long large character sums

Crystel Bujold

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Abstract

In this paper, we prove a lower bound for $\underset{\chi \neq \chi_0}{\max}\bigg|\sum_{n\leq x} \chi(n)\bigg|$, when $x= \frac{q}{(\log q)^B}$. This improves on a result of Granville and Soundararajan for large character sums when the range of summation is wide. When $B$ goes to zero, our lower bound recovers the expected maximal value of character sums for most characters.

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Crystel Bujold. 2020-05-22. Long large character sums. https://arxiv.org/abs/2005.11386

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