{
  "abstract": "Let $q=p^h>7$ be odd, put $m=(q+1)/2$, and suppose that $i=(m-2)/2$ satisfies $\\gcd(i,m)=\\gcd(i+2,m)=1$. For the $\\mathbf{F}_{q^2}$-maximal function field $\\mathcal{F}_i=\\mathbf{F}_{q^2}(x,y)$ defined by $y^m=x^i(x^2+1)$, Peter Beelen, Maria Montanucci, Jonathan Niemann, and Luciane Quoos showed that the geometric automorphism group contains a subgroup of order $4(q+1)$ and conjectured that its order is exactly $4(q+1)$. We prove this equality by establishing the reverse inequality.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03050",
  "author_total": 1,
  "authors": [
    {
      "name": "Xu Zhuang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/34ha26q43qw42.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03050",
  "fulltext_url": null,
  "id": "34ha26q43qw42",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03050",
  "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.AG"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7208732660",
  "pdf_url": "https://arxiv.org/pdf/2609.03050",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/34ha26q43qw42.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2609.03050",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03050"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "An upper bound for an exceptional automorphism group",
  "title_text": "An upper bound for an exceptional automorphism group",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/34ha26q43qw42",
  "venue": "arXiv",
  "versions": []
}