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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Determinant expression of Selberg zeta functions. III


Author: Shin-ya Koyama
Journal: Proc. Amer. Math. Soc. 113 (1991), 303-311
MSC: Primary 11F72
MathSciNet review: 1062391
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Abstract: We will prove that for $ \operatorname{PSL(2},{\mathbf{R}})$ and its cofinite subgroup, the Selberg zeta function is expressed by the determinant of the Laplacian. We will also give an explicit calculation in case of congruence subgroups, and deduce that the part of the determinant of the Laplacian composed of the continuous spectrum is expressed by Dirichlet $ L$-functions.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1062391-5
PII: S 0002-9939(1991)1062391-5
Article copyright: © Copyright 1991 American Mathematical Society