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

2023/10/27 by Yuan He, He, Yuan
Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Mathematical Approximation and Integration #Number Theory (math.NT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2310.18048

openalex publication_date 2023/10/27 · openalex created_date 2023/11/01 · openalex updated_date 2026/07/28

Abstract

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 and Jordan's totient functions. The results presented here are the generalizations of various known formulas.

Related

• Explicit formulae for the mean value of products of values of Dirichlet L-functions at positive integers
• On two mean square averages of Dirichlet L-function
• On the mean value of the generalized Dirichlet L-functions with the weight of the Gauss Sums
• Distribution of Dirichlet L-functions
• Distribution of the values of the derivative of the Dirichlet L-functions at its a-points