The density function for the value-distribution of Lerch zeta-functions and its applications

Abstract

The probabilistic study of the value-distribution of zeta-functions is one of the modern topics in analytic number theory. In this paper, we study a probability density function related to the value-distribution of Lerch zeta-functions. We prove a limit theorem with an effective error term, and moreover, we obtain an asymptotic formula on the number of zeros of Lerch zeta-functions on the right side of the critical line by applying the density function.Comment: 28 page