{
  "abstract": "The Kaneko-Zagier conjecture predicts a correspondence between finite and symmetric multiple zeta values. Under this correspondence, $ζ(3)$ corresponds to an element $Z(3)$ defined by Bernoulli numbers. We prove a conjecture of Tasaka relating $Z(3)$ to the quotient of two solutions of a recurrence. A two-index $q$-recurrence connects this quotient to a finite harmonic $q$-series. Using a method of the author, Takeyama, and Tasaka, we obtain the algebraic and analytic limits $3Z(3)/4$ and $3ζ(3)/4$ at roots of unity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18271",
  "author_total": 1,
  "authors": [
    {
      "name": "Henrik Bachmann"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6k1bvc46hh9vw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18271",
  "fulltext_url": null,
  "id": "6k1bvc46hh9vw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18271",
  "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",
      "2602|Advanced Mathematical Identities"
    ]
  ],
  "openalex": "W7213506712",
  "pdf_url": "https://arxiv.org/pdf/2609.18271",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6k1bvc46hh9vw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.18271",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18271"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A $q$-recurrence for a finite Apéry limit",
  "title_text": "A q-recurrence for a finite Apéry limit",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/6k1bvc46hh9vw",
  "venue": "arXiv",
  "versions": []
}