{"paper":{"title":"Equidistribution of Farey sequences on horospheres in covers of SL(n+1,Z)\\SL(n+1,R) and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Byron Heersink","submitted_at":"2017-12-08T19:22:42Z","abstract_excerpt":"We establish the limiting distribution of certain subsets of Farey sequences, i.e., sequences of primitive rational points, on expanding horospheres in covers $\\Delta\\backslash\\mathrm{SL}(n+1,\\mathbb{R})$ of $\\mathrm{SL}(n+1,\\mathbb{Z})\\backslash\\mathrm{SL}(n+1,\\mathbb{R})$, where $\\Delta$ is a finite index subgroup of $\\mathrm{SL}(n+1,\\mathbb{Z})$. These subsets can be obtained by projecting to the hyperplane $\\{(x_1,\\ldots,x_{n+1})\\in\\mathbb{R}^{n+1}:x_{n+1}=1\\}$ sets of the form $\\mathbf{A}=\\bigcup_{j=1}^J\\boldsymbol{a}_j\\Delta$, where for all $j$, $\\boldsymbol{a}_j$ is a primitive lattice "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.03258","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"}