Proceedings of the Japan Academy, Series A, Mathematical Sciences

A $p$-analogue of Euler’s constant and congruence zeta functions

Nobushige Kurokawa and Yuichiro Taguchi

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A $p$-analogue of a formula of Euler on the Euler constant is given, and it is interpreted in terms of the absolute zeta functions of tori.

Article information

Proc. Japan Acad. Ser. A Math. Sci., Volume 94, Number 2 (2018), 13-16.

First available in Project Euclid: 1 February 2018

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Zentralblatt MATH identifier

Primary: 11M06: $\zeta (s)$ and $L(s, \chi)$
Secondary: 11M35: Hurwitz and Lerch zeta functions 11M41: Other Dirichlet series and zeta functions {For local and global ground fields, see 11R42, 11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72} 14G10: Zeta-functions and related questions [See also 11G40] (Birch- Swinnerton-Dyer conjecture)

Euler constant $p$-analogue congruence zeta function absolute zeta function


Kurokawa, Nobushige; Taguchi, Yuichiro. A $p$-analogue of Euler’s constant and congruence zeta functions. Proc. Japan Acad. Ser. A Math. Sci. 94 (2018), no. 2, 13--16. doi:10.3792/pjaa.94.13.

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