2021 年 73 巻 3 号 p. 781-814
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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