The generalized Bernoulli numbers and its relation with the Riemann zeta function at odd-integer arguments

2023/08/24 by Yayun Wu, Wu, Yayun
Mathematics · Physics and Astronomy · #11C08 #11J72 #11M06 #30A05 #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2308.12521

openalex publication_date 2023/08/24 · openalex created_date 2023/08/26 · openalex updated_date 2026/07/28

Abstract

By using the generalized Bernoulli numbers, we deduce new integral representations for the Riemann zeta function at positive odd-integer arguments. The explicit expressions enable us to obtain criteria for the dimension of the vector space spanned over the rational by the ζ(2n+1)/π²ⁿ, n≥1.

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