{"paper":{"title":"An approximate spectral representation and explicit bounds on Green functions of Fuchsian groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Peter Bruin","submitted_at":"2012-05-29T09:09:36Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6306","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}