{"paper":{"title":"Lattice Point Counting in Sectors of Hyperbolic 3-space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Niko Laaksonen","submitted_at":"2015-11-02T16:53:56Z","abstract_excerpt":"Let $\\Gamma$ be a cocompact discrete subgroup of $\\mathrm{PSL}_{2}(\\mathbb{C})$ and denote by $\\mathcal{H}$ the three dimensional upper half-space. For a $p\\in\\mathcal{H}$, we count the number of points in the orbit $\\Gamma p$, according to their distance, $\\operatorname{arccosh} X$, from a totally geodesic hyperplane. The main term in $n$ dimensions was obtained by Herrmann for any subset of a totally geodesic submanifold. We prove a pointwise error term of $O(X^{3/2})$ by extending the method of Huber and Chatzakos-Petridis to three dimensions. By applying Chamizo's large sieve inequalities "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.00580","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"}