Abstract
We construct and study a certain zeta function which interpolates multi-poly-Bernoulli numbers at nonpositive integers and whose values at positive integers are linear combinations of multiple zeta values. This function can be regarded as the one to be paired up with the ξ-function defined by Arakawa and Kaneko. We show that both are closely related to the multiple zeta functions. Further we define multi-indexed poly-Bernoulli numbers, and generalize the duality formulas for poly-Bernoulli numbers by introducing more general zeta functions.
| Original language | English |
|---|---|
| Pages (from-to) | 19-54 |
| Number of pages | 36 |
| Journal | Nagoya Mathematical Journal |
| Volume | 232 |
| DOIs | |
| Publication status | Published - Dec 1 2018 |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
Cite this
MULTI-POLY-BERNOULLI NUMBERS AND RELATED ZETA FUNCTIONS. / Kaneko, Masanobu; Tsumura, Hirofumi.
In: Nagoya Mathematical Journal, Vol. 232, 01.12.2018, p. 19-54.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - MULTI-POLY-BERNOULLI NUMBERS AND RELATED ZETA FUNCTIONS
AU - Kaneko, Masanobu
AU - Tsumura, Hirofumi
PY - 2018/12/1
Y1 - 2018/12/1
N2 - We construct and study a certain zeta function which interpolates multi-poly-Bernoulli numbers at nonpositive integers and whose values at positive integers are linear combinations of multiple zeta values. This function can be regarded as the one to be paired up with the ξ-function defined by Arakawa and Kaneko. We show that both are closely related to the multiple zeta functions. Further we define multi-indexed poly-Bernoulli numbers, and generalize the duality formulas for poly-Bernoulli numbers by introducing more general zeta functions.
AB - We construct and study a certain zeta function which interpolates multi-poly-Bernoulli numbers at nonpositive integers and whose values at positive integers are linear combinations of multiple zeta values. This function can be regarded as the one to be paired up with the ξ-function defined by Arakawa and Kaneko. We show that both are closely related to the multiple zeta functions. Further we define multi-indexed poly-Bernoulli numbers, and generalize the duality formulas for poly-Bernoulli numbers by introducing more general zeta functions.
UR - http://www.scopus.com/inward/record.url?scp=85035315153&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85035315153&partnerID=8YFLogxK
U2 - 10.1017/nmj.2017.16
DO - 10.1017/nmj.2017.16
M3 - Article
AN - SCOPUS:85035315153
VL - 232
SP - 19
EP - 54
JO - Nagoya Mathematical Journal
JF - Nagoya Mathematical Journal
SN - 0027-7630
ER -