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1999 Multiple zeta values, poly-Bernoulli numbers, and related zeta functions
Tsuneo Arakawa, Masanobu Kaneko
Nagoya Math. J. 153(none): 189-209 (1999).

Abstract

We study the function $$\zeta(k_1,\dots,k_{n-1};s)=\sum_{0<m_1<m_2<\cdots<m_n}\frac{1}{m_1^{k_1}\cdots m_{n-1}^{k_{n-1}}m_n^{s}}$$ and show that the poly-Bernoulli numbers introduced in our previous paper are expressed as special values at negative arguments of certain combinations of these functions. As a consequence of our study, we obtain a series of relations among multiple zeta values.

Citation

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Tsuneo Arakawa. Masanobu Kaneko. "Multiple zeta values, poly-Bernoulli numbers, and related zeta functions." Nagoya Math. J. 153 189 - 209, 1999.

Information

Published: 1999
First available in Project Euclid: 27 April 2005

zbMATH: 0932.11055
MathSciNet: MR1684557

Subjects:
Primary: 11M41
Secondary: 11B68

Rights: Copyright © 1999 Editorial Board, Nagoya Mathematical Journal

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Vol.153 • 1999
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