{"paper":{"title":"Hausdorff measure of sets of Dirichlet non-improvable affine forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Taehyeong Kim, Wooyeon Kim","submitted_at":"2020-06-10T08:33:27Z","abstract_excerpt":"For a decreasing real valued function $\\psi$, a pair $(A,\\mathbf{b})$ of a real $m\\times n$ matrix $A$ and $\\mathbf{b}\\in\\mathbb{R}^m$ is said to be $\\psi$-Dirichlet improvable if the system $$\\|A\\mathbf{q}+\\mathbf{b}-\\mathbf{p}\\|^m < \\psi(T)\\quad\\text{and}\\quad\\|\\mathbf{q}\\|^n < T$$ has a solution $\\mathbf{p}\\in\\mathbb{Z}^m$, $\\mathbf{q}\\in\\mathbb{Z}^n$ for all sufficiently large $T$, where $\\|\\cdot\\|$ denotes the supremum norm. Kleinbock and Wadleigh (2019) established an integrability criterion for the Lebesgue measure of the $\\psi$-Dirichlet non-improvable set. In this paper, we prove a si"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.05727","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2006.05727/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"}