SELBERG'S TRACE FORMULA FOR THE HECKE OPERATOR GENERATED BY AN INVOLUTION, AND THE EIGENVALUES OF THE LAPLACE-BELTRAMI OPERATOR ON THE FUNDAMENTAL DOMAIN OF THE MODULAR GROUP $ PSL(2,\mathbf{Z})$

DOI10.1070/IM1978v012n03ABEH001991zbMath0416.43010OpenAlexW1991365281MaRDI QIDQ3205763

Alexei Venkov

Publication date: 1978

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

Full work available at URL: https://doi.org/10.1070/im1978v012n03abeh001991

zbMATH Keywords

Laplace-Beltrami operatordistribution of the eigenvaluesgeneralized Selberg trace formula

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Analysis on real and complex Lie groups (22E30) Modular and automorphic functions (11F03) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items

Zeta functions and periodic orbit theory: A review, A zeta function connected with the eigenvalues of the Laplace-Beltrami operator on the fundamental domain of the modular group, Distribution of prime numbers and the discrete spectrum of the Laplace operator, On the Selberg trace formula for strictly hyperbolic groups, Trace formulas for arithmetical systems, Crossing the entropy barrier of dynamical zeta functions, Zeros, eigenvalues and arithmetic, The discrete spectrum of the Laplace operator on the fundamental domain of the modular group and the Chebyshev psi-function, The Selberg trace formula for bordered Riemann surfaces