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arXiv · 2401.09935

On finite analogues of Euler's constant

Masanobu Kaneko·Toshiki Matsusaka·Shin-ichiro Seki
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Abstract

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 $\zeta(1)$'' 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.

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Masanobu Kaneko, Toshiki Matsusaka, Shin-ichiro Seki. 2024-01-18. On finite analogues of Euler's constant. https://doi.org/10.1093/imrn%2Frnae281

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