{"paper":{"title":"Pair correlation of hyperbolic lattice angles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexandru A. Popa, Alexandru Zaharescu, Florin P. Boca","submitted_at":"2013-02-20T18:46:32Z","abstract_excerpt":"Let $\\omega$ be a point in the upper half plane, and let $\\Gamma$ be a discrete, finite covolume subgroup of $\\mathrm{PSL}_2(\\mathbb{R})$. We conjecture an explicit formula for the pair correlation of the angles between geodesic rays of the lattice $\\Gamma\\omega$, intersected with increasingly large balls centered at $\\omega$. We prove this conjecture for $\\Gamma=\\mathrm{PSL}_2(\\mathbb{Z})$ and $\\omega$ an elliptic point."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5067","kind":"arxiv","version":3},"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"}