An approximate spectral representation and explicit bounds on Green functions of Fuchsian groups
Analysis of PDEs
2012-07-20 v2 Spectral Theory
Abstract
We study the Green function gr_\Gamma\ for the Laplace operator on the quotient of the hyperbolic plane by a cofinite Fuchsian group \Gamma. We use a limiting procedure, starting from the resolvent kernel, and lattice point estimates for the action of \Gamma\ on the hyperbolic plane to prove an "approximate spectral representation" for gr_\Gamma. Combining this with bounds on Maa{\ss} forms and Eisenstein series for \Gamma, we prove explicit bounds on gr_\Gamma.
Keywords
Cite
@article{arxiv.1205.6306,
title = {An approximate spectral representation and explicit bounds on Green functions of Fuchsian groups},
author = {Peter Bruin},
journal= {arXiv preprint arXiv:1205.6306},
year = {2012}
}
Comments
30 pages, plain TeX. Version 2: many additions and improvements