{
  "abstract": "We prove ten conjectures of Z.-W. Sun on Ramanujan-type series for $1/π^4$ and $π^4$ with harmonic numbers. They follow by comparing Taylor coefficients in new Borwein-Bradley-type identities, whose products depend only on $x^3$, $x^4$, $x^6$ or $x^8$. These identities come from parametric extensions of the series of Cullen and Zhao. We derive the extensions from K. C. Au's Wilf-Zeilberger (WZ) seeds, and their sums are trigonometric. Our proofs use Guillera's periodicity argument and give new proofs of the original series. In the same way, Dougall's $_5F_4$ sum gives half-integer analogues of the identities of Koecher, Borwein-Bradley and Cohen, whose Taylor coefficients are Apéry-like series for products of zeta values.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04770",
  "author_total": 1,
  "authors": [
    {
      "name": "Noam Shalev"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3bf9hd5yhbgw7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04770",
  "fulltext_url": null,
  "id": "3bf9hd5yhbgw7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04770",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CA"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Advanced Mathematical Identities"
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  "openalex": "W7220709447",
  "pdf_url": "https://arxiv.org/pdf/2610.04770",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3bf9hd5yhbgw7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.04770",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04770"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Borwein-Bradley-type identities for Ramanujan-type series for $1/π^4$",
  "title_text": "Borwein-Bradley-type identities for Ramanujan-type series for 1/π^4",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/3bf9hd5yhbgw7",
  "venue": "arXiv",
  "versions": []
}