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

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

2010-11-19

arxiv.org/abs/1011.4490v1

Mathematics

Number Theory

Scientific paper

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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