On two mean square averages of Dirichlet L-function

2021/02/17 by Neha Elizabeth Thomas, Thomas, Neha Elizabeth, Arya Chandran +3
Mathematics · #11L03 #11L05 #11M06 #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematical Approximation and Integration #Number Theory (math.NT) #math.NT #msc:11L03 #msc:11L05 #msc:11M06

paper · pdf · doi:10.48550/arxiv.2102.08844

arxiv created 2021/02/17 · openalex publication_date 2021/02/17 · arxiv updated 2021/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Finding the mean square averages of the Dirichlet L-functions over Dirichlet characters χ of same parity is an active problem in number theory. Here we explicitly evaluate such averages of L(3,χ) and L(4,χ) using certain trigonometric sums and Bernoulli polynomials and express them in terms of the Euler totient function ϕ and the Jordan totient function J_s.

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