An approximate spectral representation and explicit bounds on Green\n functions of Fuchsian groups

2012/05/29 by Peter Bruin, Bruin, Peter, Peter C. de Bruin
Mathematics · #11F72 #30F35 #35J08 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analysis of PDEs (math.AP) #Analytic Number Theory Research #FOS: Mathematics #Mathematical functions and polynomials #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1205.6306

openalex publication_date 2012/05/29 · openalex created_date 2022/09/03 · openalex updated_date 2026/07/28

Abstract

We study the Green function gr_\Γ for the Laplace operator on the\nquotient of the hyperbolic plane by a cofinite Fuchsian group \Γ. We use a\nlimiting procedure, starting from the resolvent kernel, and lattice point\nestimates for the action of \Γ on the hyperbolic plane to prove an\n"approximate spectral representation" for gr_\Γ. Combining this with bounds\non Maa ss forms and Eisenstein series for \Γ, we prove explicit bounds on\ngr_\Γ.\n

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