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 
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/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[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