{
  "abstract": "We establish weighted bilinear summation identities for two families of Apéry-like polynomials $g_n(x)$ and $v_n(x)$. The identities express weighted sums in terms of consecutive endpoint values and, when necessary, lower moments. For $g_n(x)^2$ we obtain identities with weights $(2n+1)^r$ for $1\\le r\\le4$; for $v_n(x)^2$ we treat the cubic and quintic weights. Combining these formulas with congruences for the endpoint values gives supercongruences modulo $p^3$ and $p^4$, together with special evaluations modulo $p^5$ and $p^7$, where $p$ is a prime greater than $3$. In particular, $$\\sum_{n=0}^{p-1}(2n+1)^3v_n\\!\\left(\\frac52\\right)^2 \\equiv 6p^4-\\frac{143}{3}p^6\\pmod {p^7},$$ confirming a congruence conjectured by Sun. The proofs use explicit quadratic telescoping identities and $p$-adic endpoint expansions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28098",
  "author_total": 2,
  "authors": [
    {
      "name": "Yu-Tian Li"
    },
    {
      "name": "Zhi-Hong Sun"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2s321wcgccstr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28098",
  "fulltext_url": null,
  "id": "2s321wcgccstr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28098",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Advanced Mathematical Identities"
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  ],
  "openalex": "W7214194578",
  "pdf_url": "https://arxiv.org/pdf/2609.28098",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2s321wcgccstr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.28098",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28098"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Weighted bilinear identities and supercongruences for Apéry-like polynomials",
  "title_text": "Weighted bilinear identities and supercongruences for Apéry-like polynomials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/2s321wcgccstr",
  "venue": "arXiv",
  "versions": []
}