{"paper":{"title":"Approximation to points in the plane by SL(2,Z)-orbits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Arnaldo Nogueira, Michel Laurent","submitted_at":"2010-04-08T13:14:19Z","abstract_excerpt":"Let x be a point in R^2 with irrational slope and let \\Gamma denote the lattice SL(2,Z) acting linearly on R^2. Then, the orbit \\Gamma x is dense in R^2. We give efective results on the approximation of a point y in R^2 by points of the form \\gamma x, where \\gamma belongs to \\Gamma, in terms of the size of \\gamma."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.1326","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"}