{
  "abstract": "We study the structure of the $p$-class group of the first layer of the cyclotomic $\\mathbb{Z}_p$-extension of an imaginary quadratic field where $p$ is non-split. We obtain restrictions on the growth of the cyclic factors from the base layer to the first layer; in particular, when the $p$-rank remains unchanged, each cyclic factor grows by exactly one power of $p$. We show that in a large number of cases the Iwasawa $λ$-invariant is completely determined by the $p$-rank of the first layer itself. Finally we use a Cohen-Lenstra-Martinet type philosophy to study the probability distribution of Iwasawa lambda invariants of the first layer when the base layer has cyclic $p$-class group.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10452",
  "author_total": 4,
  "authors": [
    {
      "name": "Somnath Jha"
    },
    {
      "name": "Debanjana Kundu"
    },
    {
      "name": "H. Laxmi"
    },
    {
      "name": "Lawrence C. Washington"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2bw8p0nsry7rm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10452",
  "fulltext_url": null,
  "id": "2bw8p0nsry7rm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10452",
  "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",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7220938473",
  "pdf_url": "https://arxiv.org/pdf/2610.10452",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2bw8p0nsry7rm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.10452",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10452"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "$p$-class groups in the cyclotomic $\\mathbb{Z}_p$-extension of imaginary quadratic fields",
  "title_text": "p-class groups in the cyclotomic ℤ_p-extension of imaginary quadratic fields",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/2bw8p0nsry7rm",
  "venue": "arXiv",
  "versions": []
}