Abstract
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 $GL_2(\mathbb{C})$.
Citation
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. https://doi.org/10.2969/jmsj/07017501
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