{"paper":{"title":"Uniform Diophantine approximation related to $b$-ary and $\\beta$-expansions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Lingmin Liao (LAMA), Yann Bugeaud (IRMA)","submitted_at":"2014-04-07T19:15:40Z","abstract_excerpt":"Let $b\\geq 2$ be an integer and $\\hv$ a real number. Among other results, we compute the Hausdorff dimension of the set of real numbers $\\xi$ with the property that, for every sufficiently large integer $N$, there exists an integer $n$ such that $1 \\le n \\le N$ and the distance between $b^n \\xi$ and its nearest integer is at most equal to $b^{-\\hv N}$. We further solve the same question when replacing $b^n\\xi$ by $T^n_\\beta \\xi$, where $T_\\beta$ denotes the classical $\\beta$-transformation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1889","kind":"arxiv","version":3},"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"}