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Let $q$ be a positive integer ($\geq 2$), $\chi$ be a Dirichlet charactermodulo $q$, $L(s, \chi)$ be the attached Dirichlet $L$-function, and let$L^\prime(s, \chi)$ 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 togive an asymptotic formula for the $2k$-th power mean value of$\left|(L^\prime/L)(1+it_0, \chi)\right|$ when $\chi$ runs over all Dirichletcharacters modulo $q$ (except the principal character when $t_0=0$).

An asymptotic formula for the $2k$-th power mean value of $\left| (L'/L)(1+it_0, \chi)\right|$