A discretization of the iterated integral expression of the multiple polylogarithm
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866913326217297920 |
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| author | Hirose, Minoru Matsusaka, Toshiki Seki, Shin-ichiro |
| author_facet | Hirose, Minoru Matsusaka, Toshiki Seki, Shin-ichiro |
| contents | Recently, Maesaka, Watanabe, and the third author discovered a phenomenon where the iterated integral expressions of multiple zeta values become discretized. In this paper, we extend their result to the case of multiple polylogarithms and provide two proofs. The first proof uses the method of connected sums, while the second employs induction based on the difference equations that discrete multiple polylogarithms satisfy. We also investigate several applications of our main result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_15210 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A discretization of the iterated integral expression of the multiple polylogarithm Hirose, Minoru Matsusaka, Toshiki Seki, Shin-ichiro Number Theory 11M32 Recently, Maesaka, Watanabe, and the third author discovered a phenomenon where the iterated integral expressions of multiple zeta values become discretized. In this paper, we extend their result to the case of multiple polylogarithms and provide two proofs. The first proof uses the method of connected sums, while the second employs induction based on the difference equations that discrete multiple polylogarithms satisfy. We also investigate several applications of our main result. |
| title | A discretization of the iterated integral expression of the multiple polylogarithm |
| topic | Number Theory 11M32 |
| url | https://arxiv.org/abs/2404.15210 |