{
  "abstract": "Let $E/F$ be a quadratic field extension. For any positive integer $n$ an integral hermitian form over $E/F$ is called $n$-universal if it represents all integral hermitian forms of rank $n$ over $E/F$. We study $n$-universal hermitian forms when $F$ is a local field of characteristic $\\neq 2$ or a number field. In the local case, we characterize $n$-universal integral hermitian forms and provide finite criterion sets for $n$-universality. In the number field case, we show that an indefinite integral hermitian form is $n$-universal if and only if it is $n$-universal everywhere locally.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38831",
  "author_total": 2,
  "authors": [
    {
      "name": "Yong Hu"
    },
    {
      "name": "Alexandre Lourdeaux"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d7z900cy1mnfg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38831",
  "fulltext_url": null,
  "id": "d7z900cy1mnfg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38831",
  "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/2610.38831",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d7z900cy1mnfg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38831",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38831"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Representations and $n$-universality of hermitian lattices over local and number fields",
  "title_text": "Representations and n-universality of hermitian lattices over local and number fields",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/d7z900cy1mnfg",
  "venue": "arXiv",
  "versions": []
}