{
  "abstract": "Let $p>5$ be a prime. We prove a conjecture of Z.-W. Sun asserting that $ \\sum_{k=1}^{p-1}\\frac{1}{k^4\\binom{2k}{k}} \\equiv \\frac{H_{p-1}}{p^3}-\\frac{7}{45}pB_{p-5}\\pmod{p^2}.$ As a consequence, we obtain $ \\sum_{k=1}^{p-1} \\frac{H_{k-1}^{(2)}}{k^2\\binom{2k}{k}} \\equiv \\frac{H_{p-1}}{3p^3} +\\frac{26}{135}pB_{p-5} \\pmod{p^2},$ an equivalent conjecture of K. Hessami Pilehrood and T. Hessami Pilehrood. Here $H_n^{(m)}$ denotes the generalized harmonic numbers of order $m$, with $H_n=H_n^{(1)}$, and $B_n$ denotes the $n$th Bernoulli number. The proof combines $p$-adic congruences involving harmonic numbers, finite-sum identities, and complex residue calculations via the residue theorem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30339",
  "author_total": 1,
  "authors": [
    {
      "name": "Dian-Wang Hu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/afca40enm5zyk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30339",
  "fulltext_url": null,
  "id": "afca40enm5zyk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30339",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Advanced Mathematical Identities"
    ]
  ],
  "openalex": "W7214578221",
  "pdf_url": "https://arxiv.org/pdf/2609.30339",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/afca40enm5zyk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.30339",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30339"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A Congruence Conjecture of Z.-W. Sun for Reciprocal Central Binomial Sums",
  "title_text": "A Congruence Conjecture of Z.-W. Sun for Reciprocal Central Binomial Sums",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/afca40enm5zyk",
  "venue": "arXiv",
  "versions": []
}