Two formulas for certain double and multiple polylogarithms in two variables
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910623882805248 |
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| author | Kaneko, Masanobu Tsumura, Hirofumi |
| author_facet | Kaneko, Masanobu Tsumura, Hirofumi |
| contents | We give a weighted sum formula for the double polylogarithm in two variables, from which we can recover the classical weighted sum formulas for double zeta values, double $T$-values, and some double $L$-values. Also presented is a connection-type formula for a two-variable multiple polylogarithm, which specializes to previously known single-variable formulas. This identity can also be regarded as a generalization of the renowned five-term relation for the dilogarithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_03213 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Two formulas for certain double and multiple polylogarithms in two variables Kaneko, Masanobu Tsumura, Hirofumi Number Theory 11M32, 11M99 We give a weighted sum formula for the double polylogarithm in two variables, from which we can recover the classical weighted sum formulas for double zeta values, double $T$-values, and some double $L$-values. Also presented is a connection-type formula for a two-variable multiple polylogarithm, which specializes to previously known single-variable formulas. This identity can also be regarded as a generalization of the renowned five-term relation for the dilogarithm. |
| title | Two formulas for certain double and multiple polylogarithms in two variables |
| topic | Number Theory 11M32, 11M99 |
| url | https://arxiv.org/abs/2401.03213 |