{
  "abstract": "We prove a Cohen-Lenstra type result commenting on the distribution of class group structures amongst function fields of superelliptic curves over finite fields. We also prove a result commenting on the sparsity of such superelliptic curves whose zeta functions vanish at a fixed complex number. These results are proven via point-counting techniques on certain Hurwitz schemes generalizing techniques of Ellenberg-Venkatesh-Westerland and Ellenberg-Li-Shusterman. To obtain these point counts, We prove a unitary big monodromy theorem generalizing big monodromy theorems of Yu and Achter-Pries by appealing to an arithmeticity theorem of Venkataramana.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16112",
  "author_total": 1,
  "authors": [
    {
      "name": "Hyun Jong Kim"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7cfbb004d1he2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16112",
  "fulltext_url": null,
  "id": "7cfbb004d1he2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16112",
  "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.AG"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7221772601",
  "pdf_url": "https://arxiv.org/pdf/2610.16112",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7cfbb004d1he2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.16112",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16112"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Cohen-Lenstra heuristics and vanishing of zeta functions for superelliptic curves over finite fields",
  "title_text": "Cohen-Lenstra heuristics and vanishing of zeta functions for superelliptic curves over finite fields",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/7cfbb004d1he2",
  "venue": "arXiv",
  "versions": []
}