Cramér's formula for Heisenberg manifolds
type: Item
instance of: scholarly article
title: Cramér's formula for Heisenberg manifolds
zbMATH Open document ID: 1090.58018
author: Mahta Khosravi
author: John Toth
publication date: 2006-03-24T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/116261
review text: The authors consider the difference \(R(t)\) between the counting function \(N(t)\), representing the number of eigenvalues of the Laplace Beltrami operator on a \(3\)-dimensional Heisenberg manifold which are less or equal to \(t\), and the first term of the asymptotic expansion of \(N(t)\) as \(t\) tends to \(\infty\), and prove a formula for the asymptotics of \(\int_{1}^{T}| R(t)| ^{2}\,dt\) for \(T\) large. Then a similar result is proved for Heisenberg manifolds of dimension \(2n+1\) with \(n>1\).
reviewed by: Massimo Lanza de Cristoforis
Mathematics Subject Classification ID: 58J50
Mathematics Subject Classification ID: 31C12
zbMATH DE Number: 5015296
zbMATH Keywords: Heisenberg manifolds
zbMATH Keywords: Weyl's law
zbMATH Keywords: Cramér's formula
zbMATH Keywords: Poisson summation formula
MaRDI profile type: Publication
OpenAlex ID: W2519896220
cites work: On the wave equation on a compact Riemannian manifold without conjugate points
cites work: Lattice point problems and distribution of values of quadratic forms
cites work: On the distribution of the number of lattice points inside a family of convex ovals
cites work: Integrable geodesic flows on \(n\)-step nilmanifolds
cites work: Spectre conjoint d'opérateurs pseudo-différentiels qui commutent. II. Le cas intégrable
cites work: Q5736202
cites work: Q4831655
cites work: The spectrum of positive elliptic operators and periodic bicharacteristics
cites work: Harmonic Analysis in Phase Space. (AM-122)
cites work: Q3950619
cites work: Lattice point problems and values of quadratic forms
cites work: The spectrum of the Laplacian on Riemannian Heisenberg manifolds
cites work: The spectral function of an elliptic operator
cites work: Exponential Sums and Lattice Points II
cites work: Precise spectral asymptotics for elliptic operators acting in fiberings over manifolds with boundary
cites work: The remainder in Weyl’s law for 𝑛-dimensional Heisenberg manifolds
cites work: The remainder in Weyl's law for Heisenberg manifolds
cites work: Q3142876
cites work: Improved two–term asymptotics for the eigenvalue distribution function of an elliptic operator on a compact manifold
DOI: 10.5802/AIF.2168
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 5015296