{
  "id": "1303.6507",
  "version": "v1",
  "published": "2013-03-26T14:26:45.000Z",
  "updated": "2013-03-26T14:26:45.000Z",
  "title": "A Markov model for Selmer ranks in families of twists",
  "authors": [
    "Zev Klagsbrun",
    "Barry Mazur",
    "Karl Rubin"
  ],
  "comment": "This paper is a revised version of what was originally the second half of arXiv:1111.2321v1 [math.NT]",
  "doi": "10.1112/S0010437X13007896",
  "categories": [
    "math.NT"
  ],
  "abstract": "We study the distribution of 2-Selmer ranks in the family of quadratic twists of an elliptic curve E over an arbitrary number field K. Under the assumption that Gal(K(E[2])/K) = S_3 we show that the density (counted in a non-standard way) of twists with Selmer rank r exists for all positive integers r, and is given via an equilibrium distribution, depending only on a single parameter (the `disparity'), of a certain Markov process that is itself independent of E and K. More generally, our results also apply to p-Selmer ranks of twists of 2-dimensional self-dual F_p-representations of the absolute Galois group of K by characters of order p.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-03-26T14:26:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G05",
      "11G40",
      "60J10"
    ],
    "keywords": [
      "markov model",
      "arbitrary number field",
      "absolute galois group",
      "non-standard way",
      "elliptic curve"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.6507K"
    }
  }
}