## Proceedings of the Japan Academy, Series A, Mathematical Sciences

### The Riemann hypothesis and functional equations for zeta functions over ${\bf F}_1}$

#### 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.

#### Article information

Source
Proc. Japan Acad. Ser. A Math. Sci. Volume 85, Number 6 (2009), 75-80.

Dates
First available in Project Euclid: 3 June 2009

https://projecteuclid.org/euclid.pja/1244037801

Digital Object Identifier
doi:10.3792/pjaa.85.75

Mathematical Reviews number (MathSciNet)
MR2532423

#### Citation

Kim, Sojung; Koyama, Shin-ya; Kurokawa, Nobushige. The Riemann hypothesis and functional equations for zeta functions over ${\bf F}_1}$. Proc. Japan Acad. Ser. A Math. Sci. 85 (2009), no. 6, 75--80. doi:10.3792/pjaa.85.75. https://projecteuclid.org/euclid.pja/1244037801

#### References

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