{"paper":{"title":"Hausdorff dimension of the set approximated by irrational rotations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Baowei Wang, Dong Han Kim, Micha{\\l} Rams","submitted_at":"2016-09-28T01:49:54Z","abstract_excerpt":"Let $\\theta$ be an irrational number and $\\varphi: {\\mathbb N} \\to {\\mathbb R}^{+}$ be a monotone decreasing function tending to zero. Let $$E_\\varphi(\\theta) =\\Big\\{y \\in \\mathbb R: \\|n\\theta- y\\|<\\varphi(n), \\ {\\text{for infinitely many}}\\ n\\in {\\mathbb N} \\Big\\}, $$ i.e. the set of points which are approximated by the irrational rotation with respect to the error function $\\varphi(n)$. In this article, we give a complete description of the Hausdorff dimension of $E_\\varphi(\\theta)$ for any monotone function $\\varphi$ and any irrational $\\theta$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.08724","kind":"arxiv","version":2},"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"}