Explicit formulas of the relation between multiple zeta functions of Arakawa-Kaneko and Euler-Zagier types
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913950172446720 |
|---|---|
| author | Kawasaki, Naho |
| author_facet | Kawasaki, Naho |
| contents | Multiple zeta functions of Arakawa-Kaneko and Euler-Zagier types are known as generalizations of the Riemann zeta function. In 2018, Kaneko and Tsumura proved that the multiple zeta functions of Arakawa-Kaneko type can be expressed as a ${\mathbb Q}$-linear combination of products of the ones of Euler-Zagier type and multiple zeta values. In this paper, we give explicit formulas to the above mentioned relation. Moreover, as a key of its proof, we also give certain functional equations among multi-polylogarithm functions explicitly. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_15034 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Explicit formulas of the relation between multiple zeta functions of Arakawa-Kaneko and Euler-Zagier types Kawasaki, Naho Number Theory Multiple zeta functions of Arakawa-Kaneko and Euler-Zagier types are known as generalizations of the Riemann zeta function. In 2018, Kaneko and Tsumura proved that the multiple zeta functions of Arakawa-Kaneko type can be expressed as a ${\mathbb Q}$-linear combination of products of the ones of Euler-Zagier type and multiple zeta values. In this paper, we give explicit formulas to the above mentioned relation. Moreover, as a key of its proof, we also give certain functional equations among multi-polylogarithm functions explicitly. |
| title | Explicit formulas of the relation between multiple zeta functions of Arakawa-Kaneko and Euler-Zagier types |
| topic | Number Theory |
| url | https://arxiv.org/abs/2507.15034 |