{
  "id": "2208.06862",
  "version": "v1",
  "published": "2022-08-14T14:51:06.000Z",
  "updated": "2022-08-14T14:51:06.000Z",
  "title": "A note on the distribution of Iwasawa invariants of imaginary quadratic fields",
  "authors": [
    "Anwesh Ray"
  ],
  "comment": "9 pages; original date of journal submission: 18 July 2022",
  "categories": [
    "math.NT"
  ],
  "abstract": "Given an odd prime number $p$ and an imaginary quadratic field $K$, we establish a relationship between the $p$-rank of the class group of $K$, and the classical $\\lambda$-invariant of the cyclotomic $\\mathbb{Z}_p$-extension of $K$. Exploiting this relationship, we prove statistical results for the distribution of $\\lambda$-invariants for imaginary quadratic fields ordered according to their discriminant. Some of our results are conditional since they rely on the original Cohen--Lenstra heuristics for the distribution of the $p$-parts of class groups of imaginary quadratic fields. Some results are unconditional results ad are obtained by leveraging theorems of Byeon, Craig and others.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-14T14:51:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R23"
    ],
    "keywords": [
      "imaginary quadratic field",
      "iwasawa invariants",
      "distribution",
      "class group",
      "odd prime number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}