Translator Disclaimer
July, 2021 An asymptotic formula for the $2k$-th power mean value of $|(L^{\prime}/L)(1+it_0, \chi)|$
Kohji MATSUMOTO, Sumaia SAAD EDDIN
Author Affiliations +
J. Math. Soc. Japan 73(3): 781-814 (July, 2021). DOI: 10.2969/jmsj/79987998

Abstract

Let $q$ be a positive integer ($\geq 2$), $\chi$ be a Dirichlet character modulo $q$, $L(s, \chi)$ 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 to give an asymptotic formula for the $2k$-th power mean value of $|(L^{\prime}/L)(1+it_0, \chi)|$ when $\chi$ runs over all Dirichlet characters modulo $q$ (except the principal character when $t_{0} = 0$).

Funding Statement

The first author is supported by “JSPS KAKENHI Grant Number: JP25287002”. The second author is supported by the Austrian Science Fund (FWF): Projects F5507-N26, and F5505-N26 which are parts of the special Research Program “Quasi Monte Carlo Methods: Theory and Application”. Part of this work was also done while she was supported by the Japan Society for the Promotion of Science (JSPS) “Overseas researcher under Postdoctoral Fellowship of JSPS”.

Citation

Download Citation

Kohji MATSUMOTO. Sumaia SAAD EDDIN. "An asymptotic formula for the $2k$-th power mean value of $|(L^{\prime}/L)(1+it_0, \chi)|$." J. Math. Soc. Japan 73 (3) 781 - 814, July, 2021. https://doi.org/10.2969/jmsj/79987998

Information

Received: 1 March 2018; Revised: 3 February 2020; Published: July, 2021
First available in Project Euclid: 12 April 2021

Digital Object Identifier: 10.2969/jmsj/79987998

Subjects:
Primary: 11M06
Secondary: 11Y35

Rights: Copyright ©2021 Mathematical Society of Japan

JOURNAL ARTICLE
34 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.73 • No. 3 • July, 2021
Back to Top