Selberg trace formulae for heat and wave kernels of Maass Laplacians on compact forms of the complex hyperbolic space \(H^n(\mathbb C)\), \(n\geq 2\)

DOI10.1016/S0926-2245(01)00046-8zbMath1076.11033OpenAlexW2087289469WikidataQ115338287 ScholiaQ115338287MaRDI QIDQ5945497

Khadija Ayaz, Ahmed Intissar

Publication date: 26 February 2002

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0926-2245(01)00046-8

zbMATH Keywords

Complex hyperbolic spacediscrete groupsheat and wave kernelsMaass LaplaciansSelberg traces

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Spectral theory; trace formulas (e.g., that of Selberg) (11F72) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items (6)

Quantum Hall effect on higher-dimensional spaces ⋮ Explicit formulas of the heat kernel on the quaternionic projective spaces ⋮ Integral representation of the sub-elliptic heat kernel on the complex anti-de Sitter fibration ⋮ Asymptotic of complex hyperbolic geometry and L2-spectral analysis of Landau-like Hamiltonians ⋮ Densities of generalized stochastic areas and windings arising from Anti-de Sitter and Hopf fibrations ⋮ Hartman-Watson distribution and hyperbolic-like heat kernels

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A superanalog of the Selberg trace formula and multiloop contributions for fermionic strings
• The Selberg trace formula for \(\text{PSL}(2,\mathbb R)\). Vol. 2
• On determinants of Laplacians on Riemann surfaces
• Determinants of Laplacians
• Eigenvalue problems for the Schrödinger operator with the magnetic field on a compact Riemann manifold
• Some results in \(H^ p\) theory for the Heisenberg group
• Resolvent of the Laplacian on strictly pseudoconvex domains
• \(L^2\)-concrete spectral analysis of the invariant Laplacian \(\Delta_{\alpha\beta}\) in the unit complex ball \(B^n\)
• Brownian motion on the hyperbolic plane and Selberg trace formula
• Explicit formulae for the wave kernels for the Laplacians \(\Delta_{\alpha\beta}\) in the Bergman ball \(B^ n, n\geq 1\)
• The wave kernel for the Laplacian on the classical locally symmetric spaces of rank one, theta functions, trace formulas and the Selberg zeta function. With an appendix by Andreas Juhl
• Die Differentialgleichungen in der Theorie der elliptischen Modulfunktionen. (The differential equations in the theory of elliptic modular functions)
• Fourier coefficients of the resolvent for a Fuchsian group.
• A weighted Plancherel formula II. The case of the ball
• Resolvente zum Eigenwertproblem der automorphen Formen in der hyperbolischen Ebene. I

This page was built for publication: Selberg trace formulae for heat and wave kernels of Maass Laplacians on compact forms of the complex hyperbolic space \(H^n(\mathbb C)\), \(n\geq 2\)