{"paper":{"title":"On Representation of Integers from Thin Subgroups of SL(2,Z) with Parabolics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Xin Zhang","submitted_at":"2016-10-03T22:05:48Z","abstract_excerpt":"Let $\\Lambda<SL(2,\\mathbb{Z})$ be a finitely generated, non-elementary Fuchsian group of the second kind, and $v, w$ be two primitive vectors in $\\mathbb{Z}^2-(0,0)$. We consider the set $\\mathcal{S}=\\{\\langle {v}\\gamma,{w}\\rangle_{\\mathbb{R}^2}:\\gamma\\in\\Lambda\\}$, where $\\langle\\cdot,\\cdot\\rangle_{\\mathbb{R}^2}$ is the standard inner product in $\\mathbb{R}^2$. Using Hardy-Littlewood circle method and some infinite co-volume lattice point counting techniques developed by Bourgain, Kontorovich and Sarnak, together with Gamburd's 5/6 spectral gap, we show that if $\\Lambda$ has parabolic element"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00770","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"}