Proceedings of the Japan Academy, Series A, Mathematical Sciences

Arithmetic forms of Selberg zeta functions with applications to prime geodesic theorem

Tsuneo Arakawa, Shin-ya Koyama, and Maki Nakasuji

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Abstract

We obtain an arithmetic expression of the Selberg zeta function for cocompact Fuchsian group defined via an indefinite division quaternion algebra over $\mathbf{Q}$. As application to the prime geodesic theorem, we prove certain uniformity of the distribution.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 78, Number 7 (2002), 120-125.

Dates
First available in Project Euclid: 23 May 2006

Permanent link to this document
https://projecteuclid.org/euclid.pja/1148392633

Digital Object Identifier
doi:10.3792/pjaa.78.120

Mathematical Reviews number (MathSciNet)
MR1930215

Zentralblatt MATH identifier
1027.11065

Subjects
Primary: 11R52: Quaternion and other division algebras: arithmetic, zeta functions
Secondary: 11M72 58E10: Applications to the theory of geodesics (problems in one independent variable)

Keywords
Quaternion algebra Selberg zeta function Prime geodesic theorem

Citation

Arakawa, Tsuneo; Koyama, Shin-ya; Nakasuji, Maki. Arithmetic forms of Selberg zeta functions with applications to prime geodesic theorem. Proc. Japan Acad. Ser. A Math. Sci. 78 (2002), no. 7, 120--125. doi:10.3792/pjaa.78.120. https://projecteuclid.org/euclid.pja/1148392633


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References

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