Schur type poly-Bernoulli numbers
Abstract
The poly-Bernoulli numbers and its relative are defined by the generating series using the polylogarithm series, and we call them type and , 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.
Cite
@article{arxiv.1812.10640,
title = {Schur type poly-Bernoulli numbers},
author = {Naoki Nakamura and Maki Nakasuji},
journal= {arXiv preprint arXiv:1812.10640},
year = {2018}
}