Values at non-positive integers of partially twisted multiple zeta-functions II
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915358251679744 |
|---|---|
| author | Essouabri, Driss Matsumoto, Kohji Rutard, Simon |
| author_facet | Essouabri, Driss Matsumoto, Kohji Rutard, Simon |
| contents | We study the values at non-positive integer points of multi-variable twisted multiple zeta-functions, whose each factor of the denominator is given by polynomials. The fully twisted case was already answered by de Crisenoy. On the partially twisted case, in one of our former article we studied the case when each factor of the denominator is given by linear forms or power-sum forms. In the present paper we treat the case of general polynomial denominators, and obtain explicit forms of the values at non-positive integer points. Our strategy is to reduce to the theorem of de Crisenoy for the fully twisted case, via the multiple Mellin-Barnes integral formula. We observe that in some cases the obtained values are transcendental. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_20150 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Values at non-positive integers of partially twisted multiple zeta-functions II Essouabri, Driss Matsumoto, Kohji Rutard, Simon Number Theory 11M32, 11M41 We study the values at non-positive integer points of multi-variable twisted multiple zeta-functions, whose each factor of the denominator is given by polynomials. The fully twisted case was already answered by de Crisenoy. On the partially twisted case, in one of our former article we studied the case when each factor of the denominator is given by linear forms or power-sum forms. In the present paper we treat the case of general polynomial denominators, and obtain explicit forms of the values at non-positive integer points. Our strategy is to reduce to the theorem of de Crisenoy for the fully twisted case, via the multiple Mellin-Barnes integral formula. We observe that in some cases the obtained values are transcendental. |
| title | Values at non-positive integers of partially twisted multiple zeta-functions II |
| topic | Number Theory 11M32, 11M41 |
| url | https://arxiv.org/abs/2506.20150 |