Explicit Improvements to the Burgess Bound Via P\'olya-Vinogradov

Matteo Bordignon; Forrest Francis

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arXiv · 2007.08119

Explicit Improvements to the Burgess Bound Via P\'olya-Vinogradov

Matteo Bordignon·Forrest Francis

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Abstract

We make explicit a theorem of Fromm and Goldmakher [arXiv:1706.03002], which states that one can improve Burgess' bound for short character sums simply by improving the leading constant in the P\'{o}lya-Vinogradov inequality. Towards achieving this, we establish explicit versions of several estimates related to the mean values of real multiplicative functions and the Dickman function.

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Matteo Bordignon, Forrest Francis. 2020-07-16. Explicit Improvements to the Burgess Bound Via P\'olya-Vinogradov. https://arxiv.org/abs/2007.08119

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