English

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

Number Theory 2023-08-25 v1

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\zeta(2n+1)/\pi^{2n}, n1n\geq1.

Keywords

Cite

@article{arxiv.2308.12521,
  title  = {The generalized Bernoulli numbers and its relation with the Riemann zeta function at odd-integer arguments},
  author = {Yayun Wu},
  journal= {arXiv preprint arXiv:2308.12521},
  year   = {2023}
}
R2 v1 2026-06-28T12:03:04.695Z