{"paper":{"title":"Metric Diophantine approximation on the middle-third Cantor set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.PR"],"primary_cat":"math.NT","authors_text":"Arnaud Durand (LM-Orsay), Yann Bugeaud (IRMA)","submitted_at":"2013-05-28T14:09:29Z","abstract_excerpt":"Let $\\mu\\geq 2$ be a real number and let $\\Mcal(\\mu)$ denote the set of real numbers approximable at order at least $\\mu$ by rational numbers. More than eighty years ago, Jarn\\'i k and, independently, Besicovitch established that the Hausdorff dimension of $\\Mcal(\\mu)$ is equal to $2/\\mu$. We investigate the size of the intersection of $\\Mcal(\\mu)$ with Ahlfors regular compact subsets of the interval $[0, 1]$. In particular, we propose a conjecture for the exact value of the dimension of $\\Mcal(\\mu)$ intersected with the middle-third Cantor set and give several results supporting this conjectu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6501","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"}