Distribution of the error term in the Weyl asymptotics for the Laplace operator on a two-dimensional torus and related lattice problems

DOI10.1215/S0012-7094-93-07015-9zbMath0803.11052OpenAlexW1500300291MaRDI QIDQ1320608

Pavel M. Bleher

Publication date: 3 January 1995

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-93-07015-9

zbMATH Keywords

eigenvaluesRiemannian manifoldspectral functionLaplace-Beltrami operatortwo-dimensional torusasymptotic behavior of the error term

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Global Riemannian geometry, including pinching (53C20) Lattice points in specified regions (11P21)

Related Items

Distribution of energy levels of a quantum free particle on a surface of revolution, Distribution of energy levels of quantum free particle on the Liouville surface and trace formulae, Prime lattice points in ovals, Average number of lattice points in a disk, Asymptotic of the density of states for the Schrödinger operator with periodic electric potential, Moments of the probability density functions of error terms in divisor problems, On the density of states for the periodic Schrödinger operator, Non-Gaussian energy level statistics for some integrable systems

Cites Work

• Quasi-modes sur les variétés Riemanniennes
• On the distribution of the number of lattice points inside a family of convex ovals
• Distribution of the error term for the number of lattice points inside a shifted circle
• Nombre de points entiers dans une famille homothétique de domaines de ${R}$
• The distribution and moments of the error term in the Dirichlet divisor problem
• ON THE NUMBER OF LATTICE POINTS INSIDE A RANDOM OVAL