Weyl’s law for the cuspidal spectrum of $\mathrm{SL}_n$
Annals of mathematics, Tome 165 (2007) no. 1, pp. 275-333
Voir la notice de l'article provenant de la source Annals of Mathematics website
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 $\mathrm{SL}_n(\mathbb{Z})$.
@article{10_4007_annals_2007_165_275,
author = {Werner M\"uller},
title = {Weyl{\textquoteright}s law for the cuspidal spectrum of $\mathrm{SL}_n$},
journal = {Annals of mathematics},
pages = {275--333},
publisher = {mathdoc},
volume = {165},
number = {1},
year = {2007},
doi = {10.4007/annals.2007.165.275},
mrnumber = {2276771},
zbl = {1119.11027},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2007.165.275/}
}
TY - JOUR
AU - Werner Müller
TI - Weyl’s law for the cuspidal spectrum of $\mathrm{SL}_n$
JO - Annals of mathematics
PY - 2007
SP - 275
EP - 333
VL - 165
IS - 1
PB - mathdoc
UR - http://geodesic.mathdoc.fr/articles/10.4007/annals.2007.165.275/
DO - 10.4007/annals.2007.165.275
LA - en
ID - 10_4007_annals_2007_165_275
ER -
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
Cité par Sources :