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Zbl pre06074844
McGown, Kevin J.
On the constant in Burgess' bound for the number of consecutive residues or non-residues. (English)
[J] Funct. Approximatio, Comment. Math. 46, No. 2, 273-284 (2012). ISSN 0208-6573

Summary: 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.

MSC 2000:: *11A15 Power residues, etc.
11N25 Distribution of integers with specified multiplicative constraints
11L26 Sums over arbitrary intervals
11L40 Estimates on character sums

Keywords: Dirichlet character; consecutive non-residues; power residues

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