{"paper":{"title":"Mean value results and $\\Omega$-results for the hyperbolic lattice point problem in conjugacy classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dimitrios Chatzakos","submitted_at":"2016-10-05T14:56:16Z","abstract_excerpt":"For $\\Gamma$ a Fuchsian group of finite covolume, we study the lattice point problem in conjugacy classes on the Riemann surface $\\Gamma \\backslash \\mathbb{H}$. Let $\\mathcal{H}$ be a hyperbolic conjugacy class in $\\Gamma$ and $\\ell$ the $\\mathcal{H}$-invariant closed geodesic on the surface. The main asymptotic for the counting function of the orbit $\\mathcal{H} \\cdot z$ inside a circle of radius $t$ centered at $z$ grows like $c_{\\mathcal{H}} \\cdot e^{t/2}$. This problem is also related with counting distances of the orbit of $z$ from the geodesic $\\ell$. For $X \\sim e^{t/2}$ we study mean v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01462","kind":"arxiv","version":4},"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"}