On certain mean values of logarithmic derivatives of $L$-functions and the related density functions

Masahiro Mine

Published 2018-05-28Version 1

We consider some "density function" related to the value-distribution of $L$-functions. The first example of such a density function was given by Bohr and Jessen in 1930s, who studied the case of the Riemann zeta-function. The main subject of this paper is the construction of the density function for functions in a class of $L$-functions. We prove that certain mean values of $L$-functions in the class are represented as integrals involving the related density functions.