{
  "abstract": "Let $k$ be a real quadratic field. Let $k_n$ be the $n$-th layer of the $\\mathbb{Z}_2$-extension of $k$, and $2^{a_n}$ be the $2$-part of the class number of $k_n$. In this paper, we derive many laws concerning the sequence $(a_0,a_1,\\dotsc)$, by iteratively extending the group of cyclotomic units.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.00482",
  "author_total": 1,
  "authors": [
    {
      "name": "Sosuke Sasaki"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cwm4heqky2f78.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.00482",
  "fulltext_url": null,
  "id": "cwm4heqky2f78",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.00482",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7163145539",
  "pdf_url": "https://arxiv.org/pdf/2606.00482",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cwm4heqky2f78.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2606.00482",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.00482"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On $\\mathbb{Z}_2$-extensions of real quadratic fields",
  "title_text": "On ℤ_2-extensions of real quadratic fields",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/cwm4heqky2f78",
  "venue": "arXiv",
  "versions": []
}