Geodesic
Weyl’s law for the cuspidal spectrum of $\mathrm{SL}_n$
Werner Müller1
1 Universität Bonn, Mathematisches Institut, D-53115 Bonn, Germany
Annals of mathematics, Tome 165 (2007) no. 1, pp. 275-333.

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Let $\Gamma$ be a principal congruence subgroup of $\mathrm{SL}_n(\mathbb{Z})$ and let $\sigma$ be an irreducible unitary representation of $\mathrm{SO}(n)$. Let $N^\Gamma_{\mathrm{cu}}(\lambda,\sigma)$ be the counting function of the eigenvalues of the Casimir operator acting in the space of cusp forms for $\Gamma$ which transform under $\mathrm{SO}(n)$ according to $\sigma$. In this paper we prove that the counting function $N^\Gamma_{\mathrm{cu}}(\lambda,\sigma)$ satisfies Weyl’s law. Especially, this implies that there exist infinitely many cusp forms for the full modular group $\mathrm{SL}_n(\mathbb{Z})$.
DOI : 10.4007/annals.2007.165.275

Werner Müller 1

1 Universität Bonn, Mathematisches Institut, D-53115 Bonn, Germany 
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Werner Müller. Weyl’s law for the cuspidal spectrum of $\mathrm{SL}_n$. Annals of mathematics, Tome 165 (2007) no. 1, pp. 275-333. doi : 10.4007/annals.2007.165.275. http://geodesic.mathdoc.fr/articles/10.4007/annals.2007.165.275/

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