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arXiv · 1706.03002

Improving the Burgess bound via Polya-Vinogradov

Elijah Fromm·Leo Goldmakher
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Abstract

We show that even mild improvements of the Polya-Vinogradov inequality would imply significant improvements of Burgess' bound on character sums. Our main ingredients are a lower bound on certain types of character sums (coming from works of the second author joint with J. Bober and Y. Lamzouri) and a quantitative relationship between the mean and the logarithmic mean of a completely multiplicative function.

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Elijah Fromm, Leo Goldmakher. 2017-06-09. Improving the Burgess bound via Polya-Vinogradov. https://arxiv.org/abs/1706.03002

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