Convergence of the normalized spectral counting function on degenerating hyperbolic Riemann surfaces of finite volume
type: Item
instance of: scholarly article
title: Convergence of the normalized spectral counting function on degenerating hyperbolic Riemann surfaces of finite volume
zbMATH Open document ID: 0887.58057
published in: Journal of Functional Analysis
publication date: 1997-10-26T00:00:00Z
review text: The authors study the spectral asymptotics of degenerating families of hyperbolic Riemann surfaces, either compact or non-compact but always of finite volume. They prove that the second integral of the spectral counting function has an asymptotic expansion out to \(O(l)\), where \(l\) is the degenerate parameter.
Mathematics Subject Classification ID: 58J50
Mathematics Subject Classification ID: 58J37
zbMATH DE Number: 1078490
zbMATH Keywords: degenerating hyperbolic Riemann surfaces
zbMATH Keywords: finite volume
zbMATH Keywords: spectral asymptotics
zbMATH Keywords: spectral counting function
author: Jay Jorgenson
author: Rolf E. Lundelius
reviewed by: Mircea Puta
MaRDI profile type: Publication
full work available at URL: jfan.1997.3098
OpenAlex ID: W1979763530
cites work: The real analytic theory of Teichmüller space
cites work: Degenerating families of Riemann surfaces
cites work: Q4046382
cites work: Q3310101
cites work: Q3344779
cites work: Q5284128
cites work: Spectral asymptotics on degenerating hyperbolic 3-manifolds
cites work: Q5187597
cites work: The Selberg trace formula for \(\mathrm{PSL}(2,\mathbb R)\). Vol. I
cites work: The Selberg trace formula for \(\text{PSL}(2,\mathbb R)\). Vol. 2
cites work: The Selberg trace formula and the Riemann zeta-function
cites work: On the asymptotic behavior of counting functions associated to degenerating hyperbolic Riemann surfaces
cites work: Spectral degeneration of hyperboloc Riemann surfaces
cites work: The remainder estimate in spectral accumulation for degenerating hyperbolic surfaces
cites work: CONVERGENCE OF THE HEAT KERNEL AND THE RESOLVENT KERNEL ON DEGENERATING HYPERBOLIC RIEMANN SURFACES OF FINITE VOLUME
cites work: Convergence theorems for relative spectral functions on hyperbolic Riemann surfaces of finite volume
cites work: A regularized heat trace for hyperbolic Riemann surfaces of finite volume
cites work: Asymptotics of the determinant of the Laplacian on hyperbolic surfaces of finite volume
cites work: Spectral Theory for Riemannian Manifolds with Cusps and a Related Trace Formula
cites work: Spectral geometry and scattering theory for certain complete surfaces of finite volume
cites work: Cylinders in Riemann surfaces
cites work: Q4725211
cites work: Asymptotics of the spectrum and the Selberg zeta function on the space of Riemann surfaces
DOI: 10.1006/JFAN.1997.3098
description: scientific article; zbMATH DE number 1078490