Three conjectures about character sums

Andrew Granville; Alexander P. Mangerel

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arXiv · 2112.12339

Three conjectures about character sums

Andrew Granville·Alexander P. Mangerel

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Abstract

We establish that three well-known and rather different looking conjectures about Dirichlet characters and their (weighted) sums, (concerning the P\'{o}lya-Vinogradov theorem for maximal character sums, the maximal admissible range in Burgess' estimate for short character sums, and upper bounds for $L(1,\chi)$ and $L(1+it,\chi)$) are more-or-less "equivalent". We also obtain a new mean value theorem for logarithmically weighted sums of 1-bounded multiplicative functions.

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Andrew Granville, Alexander P. Mangerel. 2021-12-23. Three conjectures about character sums. https://arxiv.org/abs/2112.12339

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