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arXiv · 1503.08353

An asymptotic distribution for $\left|L^\prime/L(1,\chi)\right|$

Sumaia Saad Eddin
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Abstract

Let $\chi$ be a Dirichlet character modulo $q$, let $L(s, \chi)$ be the attached Dirichlet $L$-function, and let $L^\prime(s, \chi)$ 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 $\left|L^\prime/L(1, \chi)\right|$ when $\chi$ ranges a primitive Dirichlet character modulo $q$ for $q$ prime. We derive some consequences, in particular a bound for the number of $\chi$ such that $\left|L^\prime/L(1, \chi)\right|$ is large.

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Sumaia Saad Eddin. 2015-03-28. An asymptotic distribution for $\left|L^\prime/L(1,\chi)\right|$. https://arxiv.org/abs/1503.08353

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