{"paper":{"title":"On the hyperbolic orbital counting problem in conjugacy classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Fr\\'ed\\'eric Paulin, Jouni Parkkonen","submitted_at":"2013-12-06T15:31:25Z","abstract_excerpt":"Given a discrete group $\\Gamma$ of isometries of a negatively curved manifold $\\widetilde M$, a nontrivial conjugacy class $\\mathfrak K$ in $\\Gamma$ and $x_0\\in\\widetilde M$, we give asymptotic counting results, as $t\\to +\\infty$, on the number of orbit points $\\gamma x_0$ at distance at most $t$ from $x_0$, when $\\gamma$ is restricted to be in $\\mathfrak K$, as well as related equidistribution results. These results generalise and extend work of Huber on cocompact hyperbolic lattices in dimension $2$. We also study the growth of given conjugacy classes in finitely generated groups endowed wit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1893","kind":"arxiv","version":1},"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"}