On the constant in Burgess' bound for the number of consecutive residues or non-residues
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2010
- DOI:
- 10.48550/arXiv.1011.4490
- arXiv:
- arXiv:1011.4490
- Bibcode:
- 2010arXiv1011.4490M
- Keywords:
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- Mathematics - Number Theory;
- 11A15;
- 11N25