{
  "abstract": "The Duffin-Schaeffer Conjecture, proven in 2020, gives a zero-full dichotomy for the approximation of irrational numbers with reduced fractions for arbitrary approximation functions. We construct approximation functions such that the inhomogeneous analogue of the Duffin-Schaeffer Conjecture fails. The counterexamples are obtained for all non-zero rationals and certain Liouville numbers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30921",
  "author_total": 3,
  "authors": [
    {
      "name": "Manuel Hauke-Treuer"
    },
    {
      "name": "James Maynard"
    },
    {
      "name": "Andrew Pollington"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3j02tdfxjgenz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30921",
  "fulltext_url": null,
  "id": "3j02tdfxjgenz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30921",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7214625913",
  "pdf_url": "https://arxiv.org/pdf/2609.30921",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3j02tdfxjgenz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.30921",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30921"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Counterexamples to the inhomogeneous Duffin-Schaeffer Conjecture",
  "title_text": "Counterexamples to the inhomogeneous Duffin-Schaeffer Conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/3j02tdfxjgenz",
  "venue": "arXiv",
  "versions": []
}