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

Yuan He

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.

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

Abstract

In this paper, we study the mean value distributions of Dirichlet -functions at positive integers. We give some explicit formulas for the mean values of products of two and three Dirichlet -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.
Paper Structure (4 sections, 9 theorems, 88 equations)

This paper contains 4 sections, 9 theorems, 88 equations.

Table of Contents

  1. Introduction
  2. Statement of main results
  3. Some auxiliary results
  4. Proofs of Theorems \ref{['thm2.1']} and \ref{['thm2.4']}

Key Result

Theorem 2.1

Let $q,m,n,a,b\in\mathbb{N}$ with $(a,q)=(b,q)=1$. Then where and

Theorems & Definitions (16)

  • Theorem 2.1
  • Corollary 2.2
  • proof
  • Corollary 2.3
  • proof
  • Theorem 2.4
  • Corollary 2.5
  • proof
  • Corollary 2.6
  • proof
  • ...and 6 more