{
  "abstract": "Let $G$ be a nontrivial finite nilpotent group. In this paper, we study the distribution of genus numbers of Galois extensions of $\\Q$ with Galois group isomorphic to $G$, ordered by absolute discriminant. We show that the proportion of fields with any prescribed genus number tends to zero, and obtain a quantitative bound for this proportion. Moreover, if every element of order $\\ell$ in $G$ is central, where $\\ell$ is the smallest prime divisor of $|G|$, we determine the orders of magnitude of the average genus number and its higher moments.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01556",
  "author_total": 2,
  "authors": [
    {
      "name": "Anup B. Dixit"
    },
    {
      "name": "Anwesh Ray"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3wvv9bea08mwf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01556",
  "fulltext_url": null,
  "id": "3wvv9bea08mwf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01556",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01556",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3wvv9bea08mwf.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01556",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01556"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Counting Nilpotent Galois extensions with prescribed genus number",
  "title_text": "Counting Nilpotent Galois extensions with prescribed genus number",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/3wvv9bea08mwf",
  "venue": "arXiv",
  "versions": []
}