ON ANALOGUES OF THE ARTIN FACTORIZATION FORMULAS IN THE SPECTRAL THEORY OF AUTOMORPHIC FUNCTIONS CONNECTED WITH INDUCED REPRESENTATIONS OF FUCHSIAN GROUPS

DOI10.1070/IM1983v021n03ABEH001800zbMath0527.10020OpenAlexW1988724987MaRDI QIDQ3043234

Peter Zograf, Alexei Venkov

Publication date: 1983

Published in: Mathematics of the USSR-Izvestiya (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/im1983v021n03abeh001800

zbMATH Keywords

Fuchsian groupsSelberg zeta-functionspectral theory of automorphic functionsArtin factorization formulasdeterminant of automorphic scattering matrix

Mathematics Subject Classification ID

Spectral theory and eigenvalue problems for partial differential equations (35P99) Modular and automorphic functions (11F03) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) (30F35)

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Square integrals of the logarithmic derivatives of Selberg’s zeta functions in the critical strip ⋮ Hecke triangle groups, transfer operators and Hausdorff dimension ⋮ Dynamical zeta functions for Artin's billiard and the Venkov-Zograf factorization formula ⋮ Euler products of Selberg zeta functions in the critical strip ⋮ Splitting density for lifting about discrete groups ⋮ Meromorphic continuation of Selberg zeta functions with twists having non-expanding cusp monodromy ⋮ Arithmetic expressions of Selberg's zeta functions for congruence subgroups ⋮ Analytic torsion for line bundles on Riemann surfaces ⋮ Artin formalism for Selberg zeta functions of co-finite Kleinian groups

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