Zeta functions over $\mathbf{F}_1$

Nobushige Kurokawa

doi:10.3792/pjaa.81.180

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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

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.

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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. https://doi.org/10.3792/pjaa.81.180