{"paper":{"title":"On Kurzweil's 0-1 Law in Inhomogeneous Diophantine Approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dong Han Kim, Michael Fuchs","submitted_at":"2015-01-20T05:42:57Z","abstract_excerpt":"We give a sufficient and necessary condition such that for almost all $s\\in{\\mathbb R}$ \\[ \\|n\\theta-s\\|<\\psi(n)\\qquad\\text{for infinitely many}\\ n\\in{\\mathbb N}, \\] where $\\theta$ is fixed and $\\psi(n)$ is a positive, non-increasing sequence. This improves upon an old result of Kurzweil and contains several previous results as special cases: two theorems of Kurzweil, a theorem of Tseng and a recent result of the second author. Moreover, we also discuss an analogue of our result in the field of formal Laurent series which has similar consequences."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04714","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"}