Determinant expression of Selberg zeta functions. II

Koyama, Shin-ya

doi:10.1090/S0002-9947-1992-1141858-0

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

Trans. Amer. Math. Soc. 329 (1992), 755-772

DOI: https://doi.org/10.1090/S0002-9947-1992-1141858-0

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Abstract:

This paper is the $\operatorname {PSL} (2,{\mathbf {C}})$-version of Part I. We show that for $\operatorname {PSL} (2,{\mathbf {C}})$ and its subgroup $\operatorname {PSL} (2,O)$, the Selberg zeta function with its gamma factors is expressed as the determinant of the Laplacians, where $O$ is the integer ring of an imaginary quadratic field. 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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