{"paper":{"title":"Zero-full law for well approximable sets in missing digit sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Bing Li, Ruofan Li, Yufeng Wu","submitted_at":"2023-02-08T08:28:11Z","abstract_excerpt":"Let $b \\geq 3$ be an integer and $C(b,D)$ be the set of real numbers in $[0,1]$ whose base $b$ expansion only consists of digits in a set $D \\subseteq \\{0,...,b-1\\}$. We study how close can numbers in $C(b,D)$ be approximated by rational numbers with denominators being powers of some integer $t$ and obtain a zero-full law for its Hausdorff measure in several circumstances. When $b$ and $t$ are multiplicatively dependent, our results correct an error of Levesley, Salp and Velani (Math. Ann., 338:97-118, 2007) and generalize their theorem. When $b$ and $t$ are multiplicatively independent but ha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.03936","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2302.03936/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"}