An approximate spectral representation and explicit bounds on Green functions of Fuchsian groups
Abstract
We study the Green function gr\ for the Laplace operator on the quotient of the hyperbolic plane by a cofinite Fuchsian group . We use a limiting procedure, starting from the resolvent kernel, and lattice point estimates for the action of \ on the hyperbolic plane to prove an "approximate spectral representation" for gr. Combining this with bounds on Maa forms and Eisenstein series for , we prove explicit bounds on gr.
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