Poly-Bernoulli numbers from shifted log-sine integrals
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917363024134144 |
|---|---|
| author | Matsusaka, Toshiki |
| author_facet | Matsusaka, Toshiki |
| contents | In 1999, Arakawa and Kaneko introduced a zeta function whose special values at negative integers yield the poly-Bernoulli numbers and investigated its relation to multiple zeta values. Since the poly-Bernoulli numbers appear in this function essentially by design, it is natural to ask whether they arise as special values of more intrinsic zeta-type objects. In this article, we show that a shifted log-sine integral provides such an example. Its analytically continued values at negative integers are given by anti-diagonal sums of poly-Bernoulli numbers with negative index. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_25392 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Poly-Bernoulli numbers from shifted log-sine integrals Matsusaka, Toshiki Number Theory In 1999, Arakawa and Kaneko introduced a zeta function whose special values at negative integers yield the poly-Bernoulli numbers and investigated its relation to multiple zeta values. Since the poly-Bernoulli numbers appear in this function essentially by design, it is natural to ask whether they arise as special values of more intrinsic zeta-type objects. In this article, we show that a shifted log-sine integral provides such an example. Its analytically continued values at negative integers are given by anti-diagonal sums of poly-Bernoulli numbers with negative index. |
| title | Poly-Bernoulli numbers from shifted log-sine integrals |
| topic | Number Theory |
| url | https://arxiv.org/abs/2603.25392 |