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

Kevin J. McGown
2012 Functiones et Approximatio Commentarii Mathematici  
We give an explicit version of a result due to D. Burgess. Let χ be a non-principal Dirichlet character modulo a prime p. We show that the maximum number of consecutive integers for which χ takes on a particular value is less than πe √ 6 3 + o(1) p 1/4 log p, where the o(1) term is given explicitly.
doi:10.7169/facm/2012.46.2.10 fatcat:wmhwaa4etvcgbl33ef2tdkrqzy