A family of integrals related to values of the Riemann zeta function

2024/09/10 by Rahul Kumar, Paul Levrie, Kumar, Rahul +5
Mathematics · #FOS: Mathematics #Mathematical Inequalities and Applications #Mathematical functions and polynomials #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2409.06546

openalex publication_date 2024/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose a relation between values of the Riemann zeta function ζ and a family of integrals. This results in an integral representation for ζ(2p), where p is a positive integer, and an expression of ζ(2p+1) involving one of the above mentioned integrals together with a harmonic-number sum. Simplification of the latter eventually leads to an integral representation of ζ(2p + 1).

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