Weak Weyl's law for congruence subgroups
| dc.creator | Labesse, Jean-Pierre | |
| dc.creator | Mueller, Werner | |
| dc.date | 2004-04-02 | |
| dc.date.accessioned | 2026-07-07T05:07:01Z | |
| dc.date.available | 2026-07-07T05:07:01Z | |
| dc.description | Let $G$ be a connected and simply connected semisimple algebraic group over $\Bbb Q$ and let $Γ\subset G(\Bbb Q)$ be an arithmetic subgroup. Let $K_\infty\subset G(\Bbb R)$ be a maximal compact subgroup and let $d$ be the dimension of the symmetric space $G({\mathbb R})/K_\infty$. Let $σ$ be an irreducible unitary representation of $K_\infty$. We prove that for every $Γ$ there exists a normal subgroup $Γ_1\subset Γ$ of finite index such that the quotient of the counting function of the $Γ_1$-cuspidal spectrum of weight $σ$ and $T^{d/2}$ has a positive lower bound as $T\to\infty$. | |
| dc.description | 13 pages | |
| dc.identifier | https://arxiv.org/abs/math/0404037 | |
| dc.identifier | http://arxiv.org/abs/math/0404037 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70695 | |
| dc.subject | Representation Theory | |
| dc.subject | Number Theory | |
| dc.subject | Spectral Theory | |
| dc.subject | 22E40; 58G25 | |
| dc.title | Weak Weyl's law for congruence subgroups | |
| dc.type | text |