Explicit formula for the spectral counting function of the Laplace operator on a compact Riemannian surface of genus \(g>1\)

DOI10.1007/S10688-012-0019-ZzbMath1277.58016OpenAlexW2075272424WikidataQ115383889 ScholiaQ115383889MaRDI QIDQ366065

D. A. Popov

Publication date: 11 September 2013

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10688-012-0019-z

zbMATH Keywords

Selberg trace formulaSelberg zeta functionarithmetic Fuchsian group \(t=\infty\)spectral counting functionstrictly hyperbolic group

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Spectral theory; trace formulas (e.g., that of Selberg) (11F72) Zero sets of holomorphic functions of several complex variables (32A60)

Related Items (1)

Spectrum of the Laplace operator on closed surfaces

Cites Work

• The Selberg trace formula and the Riemann zeta-function
• Number variance for arithmetic hyperbolic surfaces
• A geometric characterization of arithmetic Fuchsian groups.
• Introduction to modern number theory. Fundamental problems, ideas and theories. Transl. from the Russian
• SPECTRAL THEORY OF AUTOMORPHIC FUNCTIONS, THE SELBERG ZETA-FUNCTION, AND SOME PROBLEMS OF ANALYTIC NUMBER THEORY AND MATHEMATICAL PHYSICS
• A Dirichlet Series of Eigenvalue Type with Applications to Asymptotic Estimates
• Statistical properties of the spectra of Laplace-Beltrami operators on Liouville surfaces
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