{
  "abstract": "In their 1988 monograph, Conner and Hurrelbrink classified all real quadratic and biquadratic fields with odd class number. They also investigated real quadratic fields whose $2$-class numbers are equal to $2$. Their results, together with some well-known results of Ku{č}era, provide a complete classification of real quadratic number fields with $2$-class number $2$. The main aim of this paper is to provide a complete classification of all real biquadratic fields whose $2$-class numbers equal $2$; and moreover, we draw the complete list all real multiquadratic fields with odd class numbers. Finally, as an appendix we give explicit formulas for $\\sqrt{\\varepsilon_d}$, where $\\varepsilon_d$ denotes the fundamental unit of the real quadratic field $\\mathbb{Q}(\\sqrt{d})$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07180",
  "author_total": 2,
  "authors": [
    {
      "name": "Mohamed Mahmoud Chems-Eddin"
    },
    {
      "name": "Hamza El Mamry"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6z96rahjf4dpf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07180",
  "fulltext_url": null,
  "id": "6z96rahjf4dpf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07180",
  "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",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7221057437",
  "pdf_url": "https://arxiv.org/pdf/2610.07180",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6z96rahjf4dpf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.07180",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07180"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the class number of real multiquadratic fields",
  "title_text": "On the class number of real multiquadratic fields",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/6z96rahjf4dpf",
  "venue": "arXiv",
  "versions": []
}