{"paper":{"title":"Uniform Diophantine approximation with restricted denominators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Bing Li, Bo Wang, Ruofan Li","submitted_at":"2023-02-08T07:39:39Z","abstract_excerpt":"Let $b\\geq2$ be an integer and $A=(a_{n})_{n=1}^{\\infty}$ be a strictly increasing subsequence of positive integers with $\\eta:=\\limsup\\limits_{n\\to\\infty}\\frac{a_{n+1}}{a_{n}}<+\\infty$. For each irrational real number $\\xi$, we denote by $\\hat{v}_{b,A}(\\xi)$ the supremum of the real numbers $\\hat{v}$ for which, for every sufficiently large integer $N$, the equation $\\|b^{a_n}\\xi\\|<(b^{a_N})^{-\\hat{v}}$ has a solution $n$ with $1\\leq n\\leq N$. For every $\\hat{v}\\in[0,\\eta]$, let $\\hat{\\mathcal{V}}_{b,A}(\\hat{v})$ ($\\hat{\\mathcal{V}}_{b,A}^{\\ast}(\\hat{v})$) be the set of all real numbers $\\xi$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.03923","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2302.03923/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}