{"paper":{"title":"On simultaneous rational approximation to a real number and its integral powers, II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dmitry Badziahin, Yann Bugeaud","submitted_at":"2019-06-13T06:54:13Z","abstract_excerpt":"For a positive integer $n$ and a real number $\\xi$, let $\\lambda_n (\\xi)$ denote the supremum of the real numbers $\\lambda$ for which there are arbitrarily large positive integers $q$ such that $|| q \\xi ||, || q \\xi^2 ||, \\ldots , ||q \\xi^n||$ are all less than $q^{-\\lambda}$. Here, $|| \\cdot ||$ denotes the distance to the nearest integer. We establish new results on the Hausdorff dimension of the set of real numbers $\\xi$ such that $\\lambda_n (\\xi)$ is equal (or greater than or equal) to a given value."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.05508","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"}