An asymptotic formula for the 2k-th power mean value of |(L'/L)(1 + it_0,x)|

摘要

Let q be a positive integer (≥ 2), x be a Dirichlet character modulo q, L(s,x) be the attached Dirichlet L-function, and let L'(s, x) denote its derivative with respect to the complex variable s. Let t_0 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 + it_0,x)| when x runs over all Dirichlet characters modulo q (except the principal character when t_0 = 0).