Proceedings of the Japan Academy, Series A, Mathematical Sciences
- Proc. Japan Acad. Ser. A Math. Sci.
- Volume 81, Number 10 (2005), 180-184.
Zeta functions over $\mathbf{F}_1$
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

