On Limit Multiplicities for Spaces of Automorphic Forms

Deitmar, Anton ; Hoffmann, Werner

Canadian journal of mathematics, Tome 51 (1999) no. 5, pp. 952-976

Résumé

Let $\Gamma $ be a rank-one arithmetic subgroup of a semisimple Lie group $G$ . For fixed $K$ -Type, the spectral side of the Selberg trace formula defines a distribution on the space of infinitesimal characters of $G$ , whose discrete part encodes the dimensions of the spaces of square-integrable $\Gamma $ -automorphic forms. It is shown that this distribution converges to the Plancherel measure of $G$ when $\Gamma $ shrinks to the trivial group in a certain restricted way. The analogous assertion for cocompact lattices $\Gamma $ follows from results of DeGeorge-Wallach and Delorme.

Détail

DOI : 10.4153/CJM-1999-042-8

Mots-clés : 11F72, 22E30, 22E40, 43A85, 58G25, limit multiplicities, automorphic forms, noncompact quotients, Selberg trace formula, functional calculus

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