Deriving two dualities simultaneously from a family of identities for multiple harmonic sums
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909123145105408 |
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| author | Maesaka, Takumi Seki, Shin-ichiro Watanabe, Taiki |
| author_facet | Maesaka, Takumi Seki, Shin-ichiro Watanabe, Taiki |
| contents | We give a new expression of the multiple harmonic sum, which serves as a refinement of the iterated integral expression of the multiple zeta value, and prove it using the so-called connected sum method. Based on this fact, by taking two kinds of limit operations, we obtain new proofs of both the duality for multiple zeta values and the duality for finite multiple zeta values. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_05730 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Deriving two dualities simultaneously from a family of identities for multiple harmonic sums Maesaka, Takumi Seki, Shin-ichiro Watanabe, Taiki Number Theory 11M32 We give a new expression of the multiple harmonic sum, which serves as a refinement of the iterated integral expression of the multiple zeta value, and prove it using the so-called connected sum method. Based on this fact, by taking two kinds of limit operations, we obtain new proofs of both the duality for multiple zeta values and the duality for finite multiple zeta values. |
| title | Deriving two dualities simultaneously from a family of identities for multiple harmonic sums |
| topic | Number Theory 11M32 |
| url | https://arxiv.org/abs/2402.05730 |