Geodesic
Spectral Estimates for Towers of Noncompact Quotients
Canadian journal of mathematics, Tome 51 (1999) no. 2, pp. 266-293

Voir la notice de l'article provenant de la source Cambridge University Press

We prove a uniform upper estimate on the number of cuspidal eigenvalues of the $\Gamma$ -automorphic Laplacian below a given bound when $\Gamma$ varies in a family of congruence subgroups of a given reductive linear algebraic group. Each $\Gamma$ in the family is assumed to contain a principal congruence subgroup whose index in $\Gamma$ does not exceed a fixed number. The bound we prove depends linearly on the covolume of $\Gamma$ 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 $\Gamma$ .
DOI : 10.4153/CJM-1999-014-3
Mots-clés : 11F72, 58G25, 22E40 
Deitmar, Anton; Hoffman, Werner. Spectral Estimates for Towers of Noncompact Quotients. Canadian journal of mathematics, Tome 51 (1999) no. 2, pp. 266-293. doi: 10.4153/CJM-1999-014-3
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