On finite analogues of Euler's constant
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929684244070400 |
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| author | Kaneko, Masanobu Matsusaka, Toshiki Seki, Shin-ichiro |
| author_facet | Kaneko, Masanobu Matsusaka, Toshiki Seki, Shin-ichiro |
| contents | We introduce and study finite analogues of Euler's constant in the same setting as finite multiple zeta values. We define a couple of candidate values from the perspectives of a ``regularized value of $ζ(1)$'' and of Mascheroni's and Kluyver's series expressions of Euler's constant using Gregory coefficients. Moreover, we reveal that the differences between them always lie in the $\mathbb{Q}$-vector space spanned by 1 and values of a finite analogue of logarithm at positive integers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09935 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On finite analogues of Euler's constant Kaneko, Masanobu Matsusaka, Toshiki Seki, Shin-ichiro Number Theory 11M32, 11B68, 11A07 We introduce and study finite analogues of Euler's constant in the same setting as finite multiple zeta values. We define a couple of candidate values from the perspectives of a ``regularized value of $ζ(1)$'' and of Mascheroni's and Kluyver's series expressions of Euler's constant using Gregory coefficients. Moreover, we reveal that the differences between them always lie in the $\mathbb{Q}$-vector space spanned by 1 and values of a finite analogue of logarithm at positive integers. |
| title | On finite analogues of Euler's constant |
| topic | Number Theory 11M32, 11B68, 11A07 |
| url | https://arxiv.org/abs/2401.09935 |