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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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

[1] Langlangs R. P., “$L$-functions and Automorphic Representations”, Proc. Intern. Congress Math., Helsinki, 1978

[2] Venkov A. B., “Formula Artina–Takagi dlya dzeta-funktsii Selberga i gipoteza Relke”, Dokl. AN SSSR, 247:3 (1979), 540–543 | MR | Zbl

[3] Venkov A. B., Zograf P. G., “Ob analogakh formul faktorizatsii Artina v spektralnoi teorii avtomorfnykh funktsii, svyazannykh s indutsirovannymi predstavleniyami fuksovykh grupp”, Dokl. AN SSSR, 259:3 (1981), 523–526 | MR | Zbl

[4] Venkov A. B., “Spektralnaya teoriya avtomorfnykh funktsii”, Tr. Matem. in-ta im. V. A. Steklova AN SSSR, 153, 1981, 3–171 | MR | Zbl

[5] Selberg A., “Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series”, J. Indian Math. Soc., 20 (1956), 47–87 | MR | Zbl

[6] Kirillov A. A., Elementy teorii predstavlenii, Nauka, M., 1972 | MR

[7] Ray D. B., Singer I. M., “$R$-Torsion and the Laplacian on Riemannian Manifolds”, Advances in Math., 7 (1971), 145–210 | DOI | MR | Zbl