{
  "id": "1410.2921",
  "version": "v1",
  "published": "2014-10-10T22:26:34.000Z",
  "updated": "2014-10-10T22:26:34.000Z",
  "title": "Class numbers in cyclotomic Z_p-extensions",
  "authors": [
    "John C. Miller"
  ],
  "comment": "22 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "For any prime p and any positive integer n, let B(p,n) denote the n-th layer of the cyclotomic Z_p-extension over the rationals. Based on the heuristics of Cohen and Lenstra, and refined by new results on class numbers of particular B(p,n), we provide evidence for the following conjecture: For all primes p and positive integers n, the ideal class group of B(p,n) is trivial.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-10T22:26:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R29",
      "11R18",
      "11R80",
      "11Y40"
    ],
    "keywords": [
      "class numbers",
      "cyclotomic",
      "positive integer",
      "ideal class group",
      "n-th layer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.2921M"
    }
  }
}