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arXiv · 1604.05533

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

Yasushi Komori·Hirofumi Tsumura
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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 $GL_2(\mathbb{C})$.

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Yasushi Komori, Hirofumi Tsumura. 2016-04-19. On Arakawa-Kaneko zeta-functions associated with $GL_2(\mathbb{C})$ and their functional relations. https://arxiv.org/abs/1604.05533

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