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Determinant expression of Selberg zeta functions. I


Author: Shin-ya Koyama
Journal: Trans. Amer. Math. Soc. 324 (1991), 149-168
MSC: Primary 11F72; Secondary 58G26
DOI: https://doi.org/10.1090/S0002-9947-1991-1041049-7
MathSciNet review: 1041049
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Abstract: We show that for $ {\text{PSL}}(2,{\mathbf{R}})$ and its congruence subgroup, the Selberg zeta function with its gamma factors is expressed as the determinant of the Laplacian. All the gamma factors are calculated explicitly. We also give an explicit computation to the contribution of the continuous spectrum to the determinant of the Laplacian.


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DOI: https://doi.org/10.1090/S0002-9947-1991-1041049-7
Article copyright: © Copyright 1991 American Mathematical Society