On finite analogues of Euler's constant

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.

14 pages

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• Euler's constant: Euler's work and modern developments
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• Sum formula for finite multiple zeta values
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Cited by in corpus (1)

• Irrationality and transcendence questions in the "poor man's adèle ring"