Nagoya Mathematical Journal

Multiple zeta values, poly-Bernoulli numbers, and related zeta functions

Tsuneo Arakawa and Masanobu Kaneko

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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.

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Nagoya Math. J., Volume 153 (1999), 189-209.

First available in Project Euclid: 27 April 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11M41: Other Dirichlet series and zeta functions {For local and global ground fields, see 11R42, 11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72}
Secondary: 11B68: Bernoulli and Euler numbers and polynomials


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

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