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June 2009 The Riemann hypothesis and functional equations for zeta functions over ${\bf F}_1}$
Sojung Kim, Shin-ya Koyama, Nobushige Kurokawa
Proc. Japan Acad. Ser. A Math. Sci. 85(6): 75-80 (June 2009). DOI: 10.3792/pjaa.85.75

Abstract

We prove functional equations for the absolute zeta functions. We also show that the absolute zeta functions satisfy the tensor structure in the sense that their singularities possess an additive property under the tensor product. Moreover those singularities satisfy the analog of the Riemann hypothesis.

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Sojung Kim. Shin-ya Koyama. Nobushige Kurokawa. "The Riemann hypothesis and functional equations for zeta functions over ${\bf F}_1}$." Proc. Japan Acad. Ser. A Math. Sci. 85 (6) 75 - 80, June 2009. https://doi.org/10.3792/pjaa.85.75

Information

Published: June 2009
First available in Project Euclid: 3 June 2009

zbMATH: 1275.11125
MathSciNet: MR2532423
Digital Object Identifier: 10.3792/pjaa.85.75

Subjects:
Primary: 11M41

Keywords: absolute mathematics , the field with one element , zeta functions

Rights: Copyright © 2009 The Japan Academy

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Vol.85 • No. 6 • June 2009
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