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.
Citation
Kevin J. McGown. "On the constant in Burgess' bound for the number of consecutive residues or non-residues." Funct. Approx. Comment. Math. 46 (2) 273 - 284, June 2012. https://doi.org/10.7169/facm/2012.46.2.10
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