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arXiv · 1011.4490

On the constant in Burgess' bound for the number of consecutive residues or non-residues

Kevin J. McGown
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Abstract

We give an explicit version of a result due to D. Burgess. Let $\chi$ be a non-principal Dirichlet character modulo a prime $p$. We show that the maximum number of consecutive integers for which $\chi$ takes on a particular value is less than $\left\{\frac{\pi e\sqrt{6}}{3}+o(1)\right\}p^{1/4}\log p$, where the $o(1)$ term is given explicitly.

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Kevin J. McGown. 2010-11-19. On the constant in Burgess' bound for the number of consecutive residues or non-residues. https://arxiv.org/abs/1011.4490

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