{"paper":{"title":"Spectral gaps and abelian covers of convex co-compact surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Frederic Naud","submitted_at":"2018-03-09T10:08:13Z","abstract_excerpt":"Given a convex co-compact hyperbolic surface $X=\\Gamma\\backslash \\mathbb{H}^2$, we investigate the resonance spectrum $\\mathcal{R}_j$ of the laplacian $\\Delta_j$ on large finite abelian covers $X=\\Gamma_j\\backslash \\mathbb{H}^2$, where $\\Gamma_j$ is a finite index normal subgroup of $\\Gamma$. Let $\\delta$ be the Hausdorff dimension of the limit set of $\\Gamma$. We show that there exists an $\\varepsilon>0$, such that for all $j$, resonances $\\mathcal{R}_j$ in $\\{ \\delta-\\varepsilon< \\mathrm{Re}(s) \\leq \\delta \\}$ are all real and satisfy a Weyl law given by the degree of the cover i.e. $\\vert \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03446","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"}