An asymptotic distribution for |L′/L(1,χ)|

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Let χ be a Dirichlet character modulo q, let L(s, χ) be the attached Dirichlet L-function, and let L′(s, χ) denotes its derivative with respect to the complex variable s. The main purpose of this paper is to give an asymptotic formula for the 2k-th power mean value of |L′/L(1, χ)| when χ ranges a primitive Dirichlet character modulo q for q prime. We derive some consequences, in particular a bound for the number of χ such that |L′/L(1, χ)| is large.