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

2015/03/28 by Sumaia Saad Eddin, Eddin, Sumaia Saad
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #Primary 11M06 #math.NT #msc:11M06

paper · pdf · doi:10.48550/arxiv.1503.08353

17 pages, 1 figure. Submitted to the Journal of the London Mathematical Society

arxiv created 2015/03/28 · arxiv updated 2015/03/31

Abstract

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.

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