2019/08/01 by Brian Benson, Brian A. Benson, Grant S. Lakeland +4
Mathematics · #57M50 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Number Theory (math.NT) #Spectral Theory (math.SP) #math.DG #math.GT #math.NT #math.SP #msc:57M50
paper · pdf · doi:10.48550/arxiv.1908.00199
13 pages, 8 figures, 4 tables
arxiv created 2019/08/01 · openalex publication_date 2019/08/01 · arxiv updated 2019/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We compute the Cheeger constants of a collection of hyperbolic surfaces corresponding to maximal non-compact arithmetic Fuchsian groups, and to subgroups which are the rotation subgroup of maximal reflection groups. The Cheeger constants are geometric quantities, but relate to the smallest eigenvalues of Maass cusp forms. From geometrical considerations, we find evidence for the existence of small eigenvalues. We search for these small eigenvalues and compute the corresponding Maass cusp forms numerically.