{"paper":{"title":"On uniform approximation to real numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Johannes Schleischitz, Yann Bugeaud","submitted_at":"2015-12-02T17:30:54Z","abstract_excerpt":"Let $n \\ge 2$ be an integer and $\\xi$ a transcendental real number. We establish several new relations between the values at $\\xi$ of the exponents of Diophantine approximation $w_n, w_{n}^{\\ast}, \\hat{w}_{n}$, and $\\hat{w}_{n}^{\\ast}$. Combining our results with recent estimates by Schmidt and Summerer allows us to refine the inequality $\\hat{w}_{n}(\\xi) \\le 2n-1$ proved by Davenport and Schmidt in 1969."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00780","kind":"arxiv","version":4},"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"}