Spectrum of the Laplace operator on closed surfaces

DOI10.1070/RM9916zbMath1487.58030OpenAlexW4214870700MaRDI QIDQ5074409

D. A. Popov

Publication date: 9 May 2022

Published in: Russian Mathematical Surveys (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/rm9916

zbMATH Keywords

spectrumLaplace operatorgeodesic flowWeyl's formulaquantum chaosuniversality conjecturetrace formulae

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

Cites Work

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• Explicit formula for the spectral counting function of the Laplace operator on a compact Riemannian surface of genus \(g>1\)
• On the Selberg trace formula for strictly hyperbolic groups
• On the existence of limiting distributions of some number-theoretic error terms
• Sharp asymptotics of the spectrum of the Laplace operator on a manifold with periodic geodesics
• The analysis of linear partial differential operators. IV: Fourier integral operators
• Spectre conjoint d'opérateurs pseudo-différentiels qui commutent. II. Le cas intégrable
• The spectrum of positive elliptic operators and periodic bicharacteristics
• On the wave equation on a compact Riemannian manifold without conjugate points
• The Selberg trace formula and the Riemann zeta-function
• The Selberg trace formula for \(\mathrm{PSL}(2,\mathbb R)\). Vol. I
• On the wave equation asymptotics of a compact negatively curved surface
• Number variance for arithmetic hyperbolic surfaces
• Distribution of energy levels of a quantum free particle on a surface of revolution
• Formule de Poisson pour les variétés riemanniennes
• Distribution of energy levels of quantum free particle on the Liouville surface and trace formulae
• On the Weyl formula for the Laplace operator on hyperbolic Riemann surfaces
• Distribution of the error term for the number of lattice points inside a shifted circle
• The spectral function of an elliptic operator
• Curvature and the eigenvalues of the Laplacian
• Le spectre d'une variété riemannienne. (The spectrum of a Riemannian manifold)
• A remainder estimate for Weyl's law on Liouville tori
• On the second term in the Weyl formula for the spectrum of the Laplace operator on the two-dimensional torus and the number of integer points in spectral domains
• 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
• The Riemann Hypothesis for Selberg's Zeta-Function and the Asymptotic Behavior of Eigenvalues of the Laplace Operator
• Statistical properties of the spectra of Laplace-Beltrami operators on Liouville surfaces
• Quantum Chaos
• The distribution and moments of the error term in the Dirichlet divisor problem
• Circle problem and the spectrum of the Laplace operator on closed 2-manifolds
• Extremal metrics for eigenvalues of the Laplace-Beltrami operator on surfaces
• A Lower Bound for the Remainder in Weyl's Law on Negatively Curved Surfaces
• Improved two–term asymptotics for the eigenvalue distribution function of an elliptic operator on a compact manifold

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