{"paper":{"title":"A note on the Hausdorff dimension of some liminf sets appearing in simultaneous Diophantine approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Faustin Adiceam","submitted_at":"2012-09-28T12:33:55Z","abstract_excerpt":"Let Q be an infinite set of positive integers. Denote by W_{\\tau, n}(Q) (resp. W_{\\tau, n}) the set of points in dimension n simultaneously \\tau--approximable by infinitely many rationals with denominators in Q (resp. in N*). A non--trivial lower bound for the Hausdorff dimension of the liminf set W_{\\tau, n}\\W_{\\tau, n}(Q) is established when n>1 and \\tau >1+1/(n-1) in the case where the set Q satisfies some divisibility properties. The computation of the actual value of this Hausdorff dimension as well as the one--dimensional analogue of the problem are also discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.6500","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"}