{
  "abstract": "In this article, a new criterion is established to obtain the linear independence of some values of the $p$-adic Hurwitz zeta function at odd integers $s\\geq 3$. We generalize a theorem of F.~Beukers, who gave, among others, an alternative proof---using Padé approximation theory---of a result originally due to F.~Calegari on the irrationality of the $p$-adic Riemann zeta value $ζ_p(3)$ for $p = 2, 3$. To prove our main theorem, we work in a general setting, where we construct and study new Padé approximants of Laurent series satisfying the functional equation $f(z) = f(1-z)$. This complements our previous work on the linear independence of $p$-adic polygamma values.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15525",
  "author_total": 2,
  "authors": [
    {
      "name": "Makoto Kawashima"
    },
    {
      "name": "Anthony Poëls"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7peexf7wmdp2f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15525",
  "fulltext_url": null,
  "id": "7peexf7wmdp2f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15525",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Advanced Mathematical Identities"
    ]
  ],
  "openalex": "W7221784428",
  "pdf_url": "https://arxiv.org/pdf/2610.15525",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7peexf7wmdp2f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15525",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15525"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A linear independence criterion for $p$-adic Hurwitz zeta values at odd integers",
  "title_text": "A linear independence criterion for p-adic Hurwitz zeta values at odd integers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/7peexf7wmdp2f",
  "venue": "arXiv",
  "versions": []
}