Open Access
Dec. 2005 Zeta functions over $\mathbf{F}_1$
Nobushige Kurokawa
Proc. Japan Acad. Ser. A Math. Sci. 81(10): 180-184 (Dec. 2005). DOI: 10.3792/pjaa.81.180


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.


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Nobushige Kurokawa. "Zeta functions over $\mathbf{F}_1$." Proc. Japan Acad. Ser. A Math. Sci. 81 (10) 180 - 184, Dec. 2005.


Published: Dec. 2005
First available in Project Euclid: 28 December 2005

zbMATH: 1141.11316
MathSciNet: MR2196724
Digital Object Identifier: 10.3792/pjaa.81.180

Primary: 11M06

Keywords: $K$-group , one element field , stable homotopy group , zeta function

Rights: Copyright © 2005 The Japan Academy

Vol.81 • No. 10 • Dec. 2005
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