An asymptotic formula for the 2k-th power mean value of | (L'/L)(1+it₀, χ)|

2018/03/01 by Kohji Matsumoto, Matsumoto, Kohji, Sumaia Saad Eddin +1
Mathematics · #11M06 #11Y35 #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11M06 #msc:11Y35

paper · pdf · doi:10.48550/arxiv.1803.00495

35 pages, 3 figures

openalex publication_date 2018/03/01 · arxiv created 2020/02/05 · arxiv updated 2020/02/06 · openalex created_date 2020/02/14 · openalex updated_date 2026/07/28

Abstract

Let q be a positive integer (≥ 2), χ be a Dirichlet character modulo q, L(s, χ) be the attached Dirichlet L-function, and let L^′(s, χ) denote its derivative with respect to the complex variable s. Let t₀ be any fixed real number. The main purpose of this paper is to give an asymptotic formula for the 2k-th power mean value of |(L^′/L)(1+it₀, χ)| when χ runs over all Dirichlet characters modulo q (except the principal character when t₀=0).

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