On the resonances of convex co-compact subgroups of arithmetic groups

2010/11/29 by Dmitry Jakobson, Jakobson, Dmitry, Frédéric Naud +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary: 11F72 Secondary: 58J50 #Spectral Theory (math.SP) #math.AP #math.SP #msc:11F72 #msc:58J50

paper · pdf · doi:10.48550/arxiv.1011.6264

18 pages

arxiv created 2010/11/29 · arxiv updated 2010/11/30

Abstract

Let Λ be a non-elementary convex co-compact fuchsian group which is a subgroup of an arithmetic fuchsian group. We prove that the Laplace operator of the hyperbolic surface X=Λ\backslash\H has infinitely many resonances in an effective strip depending on the dimension of the limit set δ. Applications to lower bounds for the hyperbolic lattice point counting problem are derived.

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