On certain mean values of logarithmic derivatives of $L$-functions and the related density functions
Number Theory
2022-10-19 v3
Abstract
We study some "density function" related to the value-distribution of -functions. The first example of such a density function was given by Bohr and Jessen in 1930s for the Riemann zeta-function. In this paper, we construct the density function in a wide class of -functions. We prove that certain mean values of -functions in the class are represented as integrals involving the related density functions.
Keywords
Cite
@article{arxiv.1805.11072,
title = {On certain mean values of logarithmic derivatives of $L$-functions and the related density functions},
author = {Masahiro Mine},
journal= {arXiv preprint arXiv:1805.11072},
year = {2022}
}
Comments
19 pages