Explicit spectral gap for Schottky subgroups of SL (2,ℤ)

2023/03/31 by Irving Calderón, Calderón, Irving, Michael Magee +1
Mathematics · #58J50 (Primary) 11N36 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Number Theory (math.NT) #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2303.17950

openalex publication_date 2023/03/31 · openalex created_date 2023/04/06 · openalex updated_date 2026/07/28

Abstract

Let Γ be a Schottky subgroup of SL (2,ℤ). We establish a uniform and explicit lower bound of the second eigenvalue of the Laplace-Beltrami operator of congruence coverings of the hyperbolic surface Γ\backslash ℍ² provided the limit set of Γ is thick enough.

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