On the mean values of products of Dirichlet $L$-functions at positive integers

Yuan He

Published 2023-10-27Version 1

In this paper, we study the mean value distributions of Dirichlet $L$-functions at positive integers. We give some explicit formulas for the mean values of products of two and three Dirichlet $L$-functions at positive integers weighted by Dirichlet characters that involve the Bernoulli functions. The results presented here are the generalizations of various known formulas.