{"paper":{"title":"Applications of Thin Orbits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Alex Kontorovich","submitted_at":"2016-06-20T20:37:44Z","abstract_excerpt":"This text is based on a series of three expository lectures on a variety of topics related to \"thin orbits,\" as delivered at Durham University's Easter School on \"Dynamics and Analytic Number Theory\" in April 2014. The first lecture reviews closed geodesics on the modular surface and the reduction theory of binary quadratic forms before discussing Duke's equidistribution theorem (for indefinite classes). The second lecture exposits three quite different but (it turns out) not unrelated problems, due to Einsiedler-Lindenstrauss-Michel-Venkatesh, McMullen, and Zaremba. The third lecture reformul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.06325","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"}