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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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.

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

First available in Project Euclid: 23 May 2006

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Zentralblatt MATH identifier

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

Quaternion algebra Selberg zeta function Prime geodesic theorem


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.

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