{"paper":{"title":"Dirichlet uniformly well-approximated numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Dong Han Kim, Lingmin Liao (LAMA)","submitted_at":"2015-08-03T18:43:17Z","abstract_excerpt":"Fix an irrational number $\\theta$. For a real number $\\tau >0$, consider the numbers $y$ satisfying that for all large number $Q$, there exists an integer $1\\leq n\\leq Q$, such that $\\|n\\theta-y\\|<Q^{-\\tau}$, where $\\|\\cdot\\|$ is the distance of a real number to its nearest integer. These numbers are called Dirichlet uniformly well-approximated numbers. For any $\\tau>0$, the Haussdorff dimension of the set of these numbers is obtained and is shown to depend on the Diophantine property of $\\theta$. It is also proved that with respect to $\\tau$, the only possible discontinuous point of the Hausd"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00520","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"}