Determinant expression of Selberg zeta functions. III

Koyama, Shin-ya

doi:10.1090/S0002-9939-1991-1062391-5

Determinant expression of Selberg zeta functions. III
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by Shin-ya Koyama

Proc. Amer. Math. Soc. 113 (1991), 303-311

DOI: https://doi.org/10.1090/S0002-9939-1991-1062391-5

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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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