{"paper":{"title":"Large covers and sharp resonances of hyperbolic surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Dmitry Jakobson, Frederic Naud, Louis Soares","submitted_at":"2017-10-16T12:56:15Z","abstract_excerpt":"Let $\\Gamma$ be a convex co-compact discrete group of isometries of the hyperbolic plane $\\mathbb{H}^2$, and $X=\\Gamma\\backslash \\mathbb{H}^2$ the associated surface. In this paper we investigate the behaviour of resonances of the Laplacian for large degree covers of $X$ given by a finite index normal subgroup of $\\Gamma$. Using various techniques of thermodynamical formalism and representation theory, we prove two new existence results of \"sharp non-trivial resonances\" close to $\\Re(s)=\\delta_\\Gamma$, both in the large degree limit, for abelian covers and also infinite index congruence subgro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05666","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"}