{"paper":{"title":"Decoupling theorems for the Duffin-Schaeffer problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Christoph Aistleitner","submitted_at":"2019-07-10T09:37:00Z","abstract_excerpt":"The Duffin-Schaeffer conjecture is a central open problem in metric number theory. Let $\\psi~\\mathbb{N} \\mapsto \\mathbb{R}$ be a non-negative function, and set $\\mathcal{E}_n :=\\bigcup \\left( \\frac{a - \\psi(n)}{n},\\frac{a+\\psi(n)}{n} \\right)$, where the union is taken over all $a \\in \\{1, \\dots, n\\}$ which are co-prime to $n$. Then the conjecture asserts that almost all $x \\in [0,1]$ are contained in infinitely many sets $\\mathcal{E}_n$, provided that the series of the measures of $\\mathcal{E}_n$ is divergent. At the core of the conjecture is the problem of controlling the measure of the pairw"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.04590","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"}