Open Access
January, 2018 On Arakawa–Kaneko zeta-functions associated with $GL_2(\mathbb{C})$ and their functional relations
Yasushi KOMORI, Hirofumi TSUMURA
J. Math. Soc. Japan 70(1): 179-213 (January, 2018). DOI: 10.2969/jmsj/07017501


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 $GL_2(\mathbb{C})$.


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Yasushi KOMORI. Hirofumi TSUMURA. "On Arakawa–Kaneko zeta-functions associated with $GL_2(\mathbb{C})$ and their functional relations." J. Math. Soc. Japan 70 (1) 179 - 213, January, 2018.


Published: January, 2018
First available in Project Euclid: 26 January 2018

zbMATH: 06859849
MathSciNet: MR3750273
Digital Object Identifier: 10.2969/jmsj/07017501

Primary: 11B68
Secondary: 11M32

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

Rights: Copyright © 2018 Mathematical Society of Japan

Vol.70 • No. 1 • January, 2018
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