{
  "id": "1303.7337",
  "version": "v1",
  "published": "2013-03-29T09:18:54.000Z",
  "updated": "2013-03-29T09:18:54.000Z",
  "title": "The Cohen-Lenstra heuristics, moments and $p^j$-ranks of some groups",
  "authors": [
    "Christophe Delaunay",
    "Frédéric Jouhet"
  ],
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "This article deals with the coherence of the model given by the Cohen-Lenstra heuristic philosophy for class groups and also for their generalizations to Tate-Shafarevich groups. More precisely, our first goal is to extend a previous result due to E. Fouvry and J. Kl\\\"uners which proves that a conjecture provided by the Cohen-Lenstra philosophy implies another such conjecture. As a consequence of our work, we can deduce, for example, a conjecture for the probability laws of $p^j$-ranks of Selmer groups of elliptic curves. This is compatible with some theoretical works and other classical conjectures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-03-29T09:18:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conjecture",
      "cohen-lenstra heuristic philosophy",
      "cohen-lenstra philosophy implies",
      "class groups",
      "article deals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.7337D"
    }
  }
}