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

Yayun Wu

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arXiv · 2308.12521

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

Yayun Wu

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

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Yayun Wu. 2023-08-24. The generalized Bernoulli numbers and its relation with the Riemann zeta function at odd-integer arguments. https://arxiv.org/abs/2308.12521

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