Weak Weyl's law for congruence subgroups

2004/04/02 by Jean-Pierre Labesse, Labesse, Jean-Pierre, Werner Mueller +1
Mathematics · #22E40 #58G25 #Advanced Algebra and Geometry #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Number Theory (math.NT) #Representation Theory (math.RT) #Spectral Theory (math.SP) #math.NT #math.RT #math.SP #msc:22E40 #msc:58G25

paper · pdf · doi:10.48550/arxiv.math/0404037

13 pages

arxiv created 2004/04/02 · openalex publication_date 2004/04/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a connected and simply connected semisimple algebraic group over \Bbb Q and let Γ⊂ G(\Bbb Q) be an arithmetic subgroup. Let K_∞⊂ G(\Bbb R) be a maximal compact subgroup and let d be the dimension of the symmetric space G(\mathbb R)/K_∞. Let σ be an irreducible unitary representation of K_∞. We prove that for every Γ there exists a normal subgroup Γ₁⊂ Γ of finite index such that the quotient of the counting function of the Γ₁-cuspidal spectrum of weight σ and T^d/2 has a positive lower bound as T→∞.

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