2018/12/27 by Nakamura, Naoki, Nakasuji, Maki
#05E05 #11M41 #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1812.10640
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.