Geodesic
On analogues of the Artin factorization formulas in the spectral theory of automorphic functions connected with induced representations of Fuchsian groups
Izvestiya. Mathematics , Tome 21 (1983) no. 3, pp. 435-443

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This article contains proofs of the factorization formulas announced earlier for the Selberg zeta function and the determinant of an automorphic scattering matrix for arbitrary subgroups of finite index in a Fuchsian groups of the first kind. Bibliography: 7 titles. 
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     author = {A. B. Venkov and P. G. Zograf},
     title = {On analogues of the {Artin} factorization formulas in the spectral theory of automorphic functions connected with induced representations of {Fuchsian} groups},
     journal = {Izvestiya. Mathematics },
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A. B. Venkov; P. G. Zograf. On analogues of the Artin factorization formulas in the spectral theory of automorphic functions connected with induced representations of Fuchsian groups. Izvestiya. Mathematics , Tome 21 (1983) no. 3, pp. 435-443. http://geodesic.mathdoc.fr/item/IM2_1983_21_3_a1/