{
  "abstract": "We study the truncated Jacobi-symbol determinants $$\\{c,d\\}_n=\\det\\!\\left[\\left(\\frac{j^2+cjk+dk^2}{n}\\right)\\right]_{2\\le j,k\\le n-2}$$ proposed by Zhi-Wei Sun in \\cite{ZWSun} and prove Conjectures 5.1(i), 5.2, 5.3, 5.4, 5.5, 5.6(i), 5.7, 5.8, a case of 5.6(ii) of \\cite{ZWSun}, Conjecture 4.8(i) of \\cite{Sun2019} and some strengthened forms. All results follow from a single unified approach: for a prime $p$, we diagonalize the nonzero-residue matrix indexed by $\\mathbb{F}_p^\\times$ and reduce the vanishing of determinants to the supersingular reduction of certain CM elliptic curves. The same framework extends naturally to further families of parameters, suggesting a general mechanism behind identities of this type.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.08509",
  "author_total": 2,
  "authors": [
    {
      "name": "Guo Li"
    },
    {
      "name": "Xiaojun Yan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/38yvg5ggbyztv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.08509",
  "fulltext_url": null,
  "id": "38yvg5ggbyztv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.08509",
  "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.NT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2608.08509",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/38yvg5ggbyztv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2608.08509",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.08509"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On Sun's Conjectures for Truncated Jacobi-Symbol Determinants via Supersingular Elliptic Curves",
  "title_text": "On Sun's Conjectures for Truncated Jacobi-Symbol Determinants via Supersingular Elliptic Curves",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/38yvg5ggbyztv",
  "venue": "arXiv",
  "versions": []
}