Explicit formulae for the mean value of products of values of Dirichlet L-functions at positive integers

2024/05/28 by Louboutin, Stéphane
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2405.17981

Abstract

Let m≥ 1 be a rational integer. We give an explicit formula for the mean value (2)/(ϕ(f))∑_{χ(-1)=(-1)^m}\vert L(m,χ)\vert², where χ ranges over the ϕ(f)/2 Dirichlet characters modulo f>2 with the same parity as m. We then adapt our proof to obtain explicit means values for products of the form L(m₁,χ₁)⋯ L(m_n-1,χ_n-1)L(m_n,χ₁⋯χ_n-1).

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