{"paper":{"title":"Diophantine approximation on manifolds and lower bounds for Hausdorff dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Lawrence Lee, Robert C. Vaughan, Sanju Velani, Victor Beresnevich","submitted_at":"2017-12-11T13:18:03Z","abstract_excerpt":"Given $n\\in\\mathbb{N}$ and $\\tau>\\frac1n$, let $\\mathcal{S}_n(\\tau)$ denote the classical set of $\\tau$-approximable points in $\\mathbb{R}^n$, which consists of ${\\bf x}\\in \\mathbb{R}^n$ that lie within distance $q^{-\\tau-1}$ from the lattice $\\frac1q\\mathbb{Z}^n$ for infinitely many $q\\in\\mathbb{N}$. In pioneering work, Kleinbock $\\&$ Margulis showed that for any non-degenerate submanifold $\\mathcal{M}$ of $\\mathbb{R}^n$ and any $\\tau>\\frac1n$ almost all points on $\\mathcal{M}$ are not $\\tau$-approximable. Numerous subsequent papers have been geared towards strengthening this result through i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.03761","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"}