SU\G(𝔸)/K·U

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

Tsuneo Arakawa, Shin-ya Koyama, Maki Nakasuji

Type: Article

Publication Date: 2002-09-01

Citations: 9

DOI: https://doi.org/10.3792/pjaa.78.120

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.

Locations

  • Proceedings of the Japan Academy Series A Mathematical Sciences - View - PDF

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Works Cited by This (9)

Action Title Year Authors
+ Zur Zahlentheorie der Quaternionen-Algebren. 1955 Martin Eichler
+ Multiplicative Number Theory 1980 H. Davenport
+ None 2001 Andreas Strömbergsson
+ On Discontinuous Groups Operating on the Product of the Upper Half Planes 1963 Hideo Shimizu
+ A Spectral Correspondence for Maa� Waveforms 1999 Jens Bolte
Stefan Johansson
+ PDF Chat The dimension of the space of cusp forms on the Siegel upper half plane of degree two related to a quaternion unitary group 1981 Tsuneo Arakawa
+ Class numbers of indefinite binary quadratic forms 1982 Peter Sarnak
+ Prime geodesic theorem. 1984 Henryk Iwaniec
+ PDF Chat The Selberg Trace Formula for PSL(2,ℝ) 1983 Dennis A. Hejhal