{"paper":{"title":"The Duffin-Schaeffer conjecture with a moving target","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Felipe A. Ramirez, Manuel Hauke","submitted_at":"2024-07-07T12:35:02Z","abstract_excerpt":"We prove the inhomogeneous generalization of the Duffin-Schaeffer conjecture in dimension $m \\geq 3$. That is, given $\\mathbf{y}\\in \\mathbb{R}^m$ and $\\psi:\\mathbb{N}\\to\\mathbb{R}_{\\geq 0}$ such that $\\sum (\\varphi(q)\\psi(q)/q)^m = \\infty$, we show that for almost every $\\mathbf{x} \\in\\mathbb{R}^m$ there are infinitely many rational vectors $\\mathbf{a}/q$ such that $\\vert q\\mathbf{x} - \\mathbf{a} - \\mathbf{y}\\vert<\\psi(q)$ and such that each component of $\\mathbf{a}$ is coprime to $q$. This is an inhomogeneous extension of a homogeneous conjecture of Sprind\\v{z}uk which was itself proved in 19"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.05344","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.05344/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"}