Journal of the Mathematical Society of Japan

On Arakawa–Kaneko zeta-functions associated with $GL_2(\mathbb{C})$ and their functional relations

Yasushi KOMORI and Hirofumi TSUMURA

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We construct a certain class of Arakawa–Kaneko zeta-functions associated with $GL_2(\mathbb{C})$, which includes the ordinary Arakawa–Kaneko zeta-function. We also define poly-Bernoulli polynomials associated with $GL_2(\mathbb{C})$ which appear in their special values of these zeta-functions. We prove some functional relations for these zeta-functions, which are regarded as interpolation formulas of various relations among poly-Bernoulli numbers. Considering their special values, we prove difference relations and duality relations for poly-Bernoulli polynomials associated with $GL_2(\mathbb{C})$.

Article information

J. Math. Soc. Japan, Volume 70, Number 1 (2018), 179-213.

First available in Project Euclid: 26 January 2018

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Zentralblatt MATH identifier

Primary: 11B68: Bernoulli and Euler numbers and polynomials
Secondary: 11M32: Multiple Dirichlet series and zeta functions and multizeta values

Arakawa–Kaneko zeta-functions poly-Bernoulli numbers polylogarithms Lerch transcendent


KOMORI, Yasushi; TSUMURA, Hirofumi. On Arakawa–Kaneko zeta-functions associated with $GL_2(\mathbb{C})$ and their functional relations. J. Math. Soc. Japan 70 (2018), no. 1, 179--213. doi:10.2969/jmsj/07017501.

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