{
  "abstract": "Let $q$ be a prime power and $\\mathbb{F}_{q^2}$ be the finite fields of $q^2$ elements. The Hermitian function field $H=\\mathbb{F}_{q^2}(x,y)$ defined by $y^q+y=x^{q+1}$ is a well-known maximal function field with the largest possible genus. Let $A(P_\\infty)$ be the decomposition group of the infinity place $P_\\infty$ of $H$ which is the common pole of $x$ and $y$. For every subgroup $G\\le A(P_\\infty)$, we construct explicit generators of Galois subfield $H^G$ of $H$ with respect to $G$ and determine an absolutely irreducible equation defining the smooth affine plane model for such a Galois subfield. For $p$-subgroups, the generators can be chosen so that the defining equation has an additive polynomial on the left-hand side and an $\\mathbb{F}_p$-quadratic polynomial on the right-hand side. For $q=27$, we can construct a genus-two subfield $D\\subset H$ that is not isomorphic to $H^J$ for any subgroup $J\\le \\text{Aut}(H)$ from the explicit equations of Galois subfields of the Hermitian function field. To the best of our knowledge, this is the first example of a maximal function field covered but not Galois-covered by the same Hermitian function field.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19095",
  "author_total": 2,
  "authors": [
    {
      "name": "Liming Ma"
    },
    {
      "name": "Yipeng Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9g9wc1en8a3x6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19095",
  "fulltext_url": null,
  "id": "9g9wc1en8a3x6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19095",
  "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.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7213530541",
  "pdf_url": "https://arxiv.org/pdf/2609.19095",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9g9wc1en8a3x6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.19095",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19095"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Explicit equations of Galois subfields of Hermitian function fields with respect to decomposition groups",
  "title_text": "Explicit equations of Galois subfields of Hermitian function fields with respect to decomposition groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/9g9wc1en8a3x6",
  "venue": "arXiv",
  "versions": []
}