Limit multiplicities for \rm SL₂(O_F) in \rm SL₂(ℝ^r₁⊕ℂ^r₂)

2017/02/20 by Jasmin Matz, Matz, Jasmin
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1702.06170

33 pages

openalex publication_date 2017/02/20 · arxiv created 2018/06/12 · arxiv updated 2018/06/13 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

We prove that the family of lattices \rm SL₂(O_F), F running over number fields with fixed archimedean signature (r₁, r₂), in \rm SL₂(ℝ^r₁⊕ℂ^r₂) has the limit multiplicity property.

Citations

• Asymptotic behavior of supercuspidal representations and Sato-Tate equidistribution for families

Cited by

• Strong limit multiplicity for arithmetic hyperbolic surfaces and 3-manifolds

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