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An asymptotic formula for the $2k$-th power mean value of $\left| (L'/L)(1+it_0, ��)\right|$
DOI
Open Access
Description
Let $q$ be a positive integer ($\geq 2$), $��$ be a Dirichlet character modulo $q$, $L(s, ��)$ be the attached Dirichlet $L$-function, and let $L^\prime(s, ��)$ 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 $\left|(L^\prime/L)(1+it_0, ��)\right|$ when $��$ runs over all Dirichlet characters modulo $q$ (except the principal character when $t_0=0$).
35 pages, 3 figures
