{"paper":{"title":"Resolvent of the Laplacian on geometrically finite hyperbolic manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SP","authors_text":"Colin Guillarmou (DMA), Rafe Mazzeo","submitted_at":"2010-02-10T18:29:28Z","abstract_excerpt":"For geometrically finite hyperbolic manifolds $\\Gamma\\backslash H^{n+1}$, we prove the meromorphic extension of the resolvent of Laplacian, Poincar\\'e series, Einsenstein series and scattering operator to the whole complex plane. We also deduce the asymptotics of lattice points of $\\Gamma$ in large balls of $H^{n+1}$ in terms of the Hausdorff dimension of the limit set of $\\Gamma$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.2165","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"}