The generalized Bernoulli numbers and its relation with the Riemann zeta function at odd-integer arguments
Year: 2023
Type: preprint
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 $ζ(2n+1)/π^{2n}$, $n\geq1$.
Source: arXiv (Cornell University)
Author: Wu, Yayun
Institution: Hefei Normal University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4386185140