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arXiv · 1812.10640

Schur type poly-Bernoulli numbers

Naoki Nakamura·Maki Nakasuji
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Abstract

The poly-Bernoulli numbers and its relative are defined by the generating series using the polylogarithm series, and we call them type $B$ and $C$, respectively. As a generalization of these poly-Bernoulli numbers, we introduce Schur type poly-Bernoulli numbers and investigate their properties. First, we define a generalization of Arakawa-Kaneko multiple zeta functions and obtain their expression in terms of Schur type Bernoulli numbers. Next, under the restriction to the hook type, we define a generalization of Kaneko-Tsumura multiple zeta functions and obtain similar expression in terms of Schur type Bernoulli numbers. Lastly, we study more properties such as a recurrence formula, a relation formula between Bernoulli numbers and a description in terms of the Stirling numbers.

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Naoki Nakamura, Maki Nakasuji. 2018-12-27. Schur type poly-Bernoulli numbers. https://arxiv.org/abs/1812.10640

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