On analogues of the Artin factorization formulas in the spectral theory of automorphic functions connected with induced representations of Fuchsian groups

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.