{"paper":{"title":"Badly approximable vectors in affine subspaces: Jarn\\'{\\i}k-type result","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Nikolay Moshchevitin","submitted_at":"2011-02-22T08:27:37Z","abstract_excerpt":"Consider irrational affine subspace $ A\\subset \\mathbb{R}^d$ of dimension $a$. We prove that the set $$ \\{\\xi =(\\xi_1,...,\\xi_d) \\in {A}:\\,\\,\\, \\ q^{1/a}\\cdot \\max_{1\\le i \\le d} ||q\\xi_i|| \\to \\infty,\\,\\,\\,\\, q\\to \\infty\\} $$ is an $\\alpha$-winning set for every $\\alpha \\in (0,1/2]$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4431","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"}