{"paper":{"title":"Inhomogeneous Diophantine approximation with general error functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Lingmin Liao (LAMA), Michal Rams (PAN)","submitted_at":"2012-08-09T07:04:52Z","abstract_excerpt":"Let $\\al$ be an irrational and $\\varphi: \\N \\rightarrow \\R^+$ be a function decreasing to zero. For any $\\al$ with a given Diophantine type, we show some sharp estimations for the Hausdorff dimension of the set [E_{\\varphi}(\\al):={y\\in \\R: |n\\al -y| < \\varphi(n) \\text{for infinitely many} n},] where $|\\cdot|$ denotes the distance to the nearest integer."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1826","kind":"arxiv","version":3},"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"}