Nagoya Mathematical Journal

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

Tsuneo Arakawa and Masanobu Kaneko

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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.

Article information

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

Dates
First available in Project Euclid: 27 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1114630825

Mathematical Reviews number (MathSciNet)
MR1684557

Zentralblatt MATH identifier
0932.11055

Subjects
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

Citation

Arakawa, Tsuneo; Kaneko, Masanobu. Multiple zeta values, poly-Bernoulli numbers, and related zeta functions. Nagoya Math. J. 153 (1999), 189--209. https://projecteuclid.org/euclid.nmj/1114630825


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