Proceedings of the Japan Academy, Series A, Mathematical Sciences

Zeta functions over $\mathbf{F}_1$

Nobushige Kurokawa

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Abstract

We show basic properties of zeta functions over the one element field starting from an algebraic set over the integer ring. We calculate several examples and we investigate special values via the associated $K$-group identified as the stable homotopy group of spheres.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 81, Number 10 (2005), 180-184.

Dates
First available in Project Euclid: 28 December 2005

Permanent link to this document
https://projecteuclid.org/euclid.pja/1135791771

Digital Object Identifier
doi:10.3792/pjaa.81.180

Mathematical Reviews number (MathSciNet)
MR2196724

Zentralblatt MATH identifier
1141.11316

Subjects
Primary: 11M06: $\zeta (s)$ and $L(s, \chi)$

Keywords
Zeta function one element field $K$-group stable homotopy group

Citation

Kurokawa, Nobushige. Zeta functions over $\mathbf{F}_1$. Proc. Japan Acad. Ser. A Math. Sci. 81 (2005), no. 10, 180--184. doi:10.3792/pjaa.81.180. https://projecteuclid.org/euclid.pja/1135791771


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