{
  "abstract": "Let $k$ be a field of characteristic $\\neq 2$. Under suitable assumptions on the dimensions of anisotropic quadratic forms over $k$ and $k(x)$, we show that a definite integral quadratic form over the polynomial ring $k[x]$ is universal if the form represents all scalars from $k$ and all scalar multiples of $x$. The coefficient field $k$ in our main result can be a finite field, a non-dyadic higher local field, a global function field, or a one-variable function field over $\\mathbb{C}$ or $\\mathbb{C}(t)$. We have a finite universality criterion set over $k[x]$ for some coefficient fields $k$, including some cases where $k$ has infinitely many square classes (e.g., $k=\\mathbb{C}(t)$).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37339",
  "author_total": 2,
  "authors": [
    {
      "name": "Yong Hu"
    },
    {
      "name": "Jing Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7dh6hjxcabn4d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37339",
  "fulltext_url": null,
  "id": "7dh6hjxcabn4d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37339",
  "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",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7224131578",
  "pdf_url": "https://arxiv.org/pdf/2610.37339",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7dh6hjxcabn4d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.37339",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37339"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Universality Criterion Sets for Definite Quadratic Lattices over Polynomial Rings",
  "title_text": "Universality Criterion Sets for Definite Quadratic Lattices over Polynomial Rings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/7dh6hjxcabn4d",
  "venue": "arXiv",
  "versions": []
}