location:  Publications → journals → CJM
Abstract view

# Spectral Estimates for Towers of Noncompact Quotients

Published:1999-04-01
Printed: Apr 1999
• Anton Deitmar
• Werner Hoffman
 Format: HTML LaTeX MathJax PDF PostScript

## Abstract

We prove a uniform upper estimate on the number of cuspidal eigenvalues of the $\Ga$-automorphic Laplacian below a given bound when $\Ga$ varies in a family of congruence subgroups of a given reductive linear algebraic group. Each $\Ga$ in the family is assumed to contain a principal congruence subgroup whose index in $\Ga$ does not exceed a fixed number. The bound we prove depends linearly on the covolume of $\Ga$ and is deduced from the analogous result about the cut-off Laplacian. The proof generalizes the heat-kernel method which has been applied by Donnelly in the case of a fixed lattice~$\Ga$.
 MSC Classifications: 11F72 - Spectral theory; Selberg trace formula 58G25 - unknown classification 58G2522E40 - Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx]

 top of page | contact us | privacy | site map |