{
  "abstract": "Fauzan's determinantal proof that $ζ(5)$ is irrational also yields $|ζ(5)-a/b|>b^{-260}$ for all large $b$. The exponent is the product $\\varrhoλ/\\varepsilon$ of three constants attached to the construction, of which $\\varrho$ governs the growth of a relative matrix norm. We show that $\\varrho$ may be taken to be $9.09$ instead of $6933/500=13.866$, and deduce $|ζ(5)-a/b|>b^{-171}$ for all integers $a$ and all sufficiently large integers $b$, so that the irrationality exponent of $ζ(5)$ is at most $171$. Two closed-form functions replace two worst-case estimates: a node function, which bounds the residue weights individually instead of uniformly, and the external field of the energy estimate, which replaces a factor-by-factor bound on the weight. The result is conditional on Fauzan's preprint. An exact arithmetic verifier is attached.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01708",
  "author_total": 1,
  "authors": [
    {
      "name": "David Niedbala Giraudin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6725tvy4eeqwb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01708",
  "fulltext_url": null,
  "id": "6725tvy4eeqwb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01708",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01708",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6725tvy4eeqwb.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01708",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01708"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A new upper bound for the irrationality exponent of $ζ(5)$",
  "title_text": "A new upper bound for the irrationality exponent of ζ(5)",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/6725tvy4eeqwb",
  "venue": "arXiv",
  "versions": []
}