{"paper":{"title":"Improved fractal Weyl bounds for hyperbolic manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.SP","authors_text":"David Borthwick, Semyon Dyatlov, Tobias Weich","submitted_at":"2015-12-02T20:38:55Z","abstract_excerpt":"We give a new fractal Weyl upper bound for resonances of convex co-compact hyperbolic manifolds in terms of the dimension $n$ of the manifold and the dimension $\\delta$ of its limit set. More precisely, we show that as $R\\to\\infty$, the number of resonances in the box $[R,R+1]+i[-\\beta,0]$ is $O(R^{m(\\beta,\\delta)+})$, where the exponent $m(\\beta,\\delta)=\\min(2\\delta+2\\beta+1-n,\\delta)$ changes its behavior at $\\beta=(n-1-\\delta)/2$. In the case $\\delta<(n-1)/2$, we also give an improved resolvent upper bound in the standard resonance free strip $\\{\\mathrm{Im}\\ \\lambda\\ > \\delta-(n-1)/2\\}$. Bo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00836","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"}