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

2010/11/19 by Kevin J. McGown, McGown, Kevin J.
Mathematics · #11A15 #11N25 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT) #math.NT #msc:11A15 #msc:11N25

paper · pdf · doi:10.48550/arxiv.1011.4490

arxiv created 2010/11/19 · openalex publication_date 2010/11/19 · arxiv updated 2010/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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^1/4log p, where the o(1) term is given explicitly.

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