Sign changes of the error term in Weyl’s law for Heisenberg manifolds

DOI10.1090/S0002-9947-2012-05437-7zbMath1241.11119OpenAlexW2051214686MaRDI QIDQ5390255

Zhai, Wenguang, Kai-Man Tsang

Publication date: 27 April 2012

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-2012-05437-7

zbMATH Keywords

error termHeisenberg manifoldWeyl's lawshort intervalssign changeVoronoi's formula

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Asymptotic results on counting functions for algebraic and topological structures (11N45) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Asymptotic distributions of eigenvalues in context of PDEs (35P20)

Related Items (3)

Sign changes of \(\Delta_{(1)}(x)\) ⋮ Recent progress on the Dirichlet divisor problem and the mean square of the Riemann zeta-function ⋮ On the Dirichlet divisor problem in short intervals

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Higher moments of the error term in the divisor problem
• Cramér's formula for Heisenberg manifolds
• A lower bound for the error term in Weyl's law for certain Heisenberg manifolds
• The spectrum of the Laplacian on Riemannian Heisenberg manifolds
• On the distribution of the number of lattice points inside a family of convex ovals
• On the wave equation on a compact Riemannian manifold without conjugate points
• Ein \(\Omega\)-Resultat für das quadratische Mittel der Riemannschen Zetafunktion auf der kritischen Linie
• Sign changes of \(E(T)\), \(\Delta(x)\), and \(P(x)\)
• The remainder in Weyl's law for Heisenberg manifolds
• Lattice point problems and values of quadratic forms
• Lattice point problems and distribution of values of quadratic forms
• The spectral function of an elliptic operator
• On the error term in Weyl's law for Heisenberg manifolds
• On the mean square formula of the error term in the Dirichlet divisor problem
• Harmonic Analysis in Phase Space. (AM-122)
• Exponential Sums and Lattice Points III
• On higher-power moments of Δ(x) (II)
• Higher-Power Moments of δ(x ), E(t ) and P(x )
• The remainder in Weyl’s law for 𝑛-dimensional Heisenberg manifolds
• On higher-power moments of Δ(x) (III)
• Improved two–term asymptotics for the eigenvalue distribution function of an elliptic operator on a compact manifold

This page was built for publication: Sign changes of the error term in Weyl’s law for Heisenberg manifolds