{
  "abstract": "For a finite group $G$, define the field $\\mathbb{Q}(G) := \\mathbb{Q}(\\{χ(g) : χ\\in \\operatorname{Irr}(G) , g \\in G\\})$. In this article we compute generating sets for the fields $\\mathbb{Q}(G)$ when $G$ is a finite general or special linear group, a finite general or special unitary group, or one of the simple groups $\\operatorname{PSL}_n(q)$ or $\\operatorname{PSU}_n(q)$. We then apply these results to classify all number fields $F$ of degree $2$ or $3$ over $\\mathbb{Q}$ such that $F = \\mathbb{Q}(S)$ for some non-abelian simple group $S$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35183",
  "author_total": 1,
  "authors": [
    {
      "name": "Eden Ketchum"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fq1k06hbwsm9s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35183",
  "fulltext_url": null,
  "id": "fq1k06hbwsm9s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35183",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7214802166",
  "pdf_url": "https://arxiv.org/pdf/2609.35183",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fq1k06hbwsm9s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.35183",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35183"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The fields generated by character values of linear and unitary groups",
  "title_text": "The fields generated by character values of linear and unitary groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/fq1k06hbwsm9s",
  "venue": "arXiv",
  "versions": []
}