{
  "id": "1005.1458",
  "version": "v3",
  "published": "2010-05-10T06:34:04.000Z",
  "updated": "2016-05-17T02:07:59.000Z",
  "title": "Equidistribution of bounded torsion CM points",
  "authors": [
    "Bob Hough"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Averaging over imaginary quadratic fields, we prove, quantitatively, the equidistribution of CM points associated to 3-torsion classes in the class group. We conjecture that this equidistribution holds for points associated to ideals of any fixed odd order. We prove a partial equidistribution result in this direction and present empirical evidence.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-05-12T01:22:02.000Z",
      "title": "Average equidistribution of Heegner points associated to the 3-part of the class group of imaginary quadratic fields",
      "abstract": "We prove that the Heegner points attached to the 3-part of the class group of an imaginary quadratic field $\\Q(\\sqrt{-d})$ equidistribute in $\\mathcal{F} = SL_2(\\zed)\\backslash \\uH$ on average over $d$ as $d \\to \\infty$. As a result, we obtain a proof of the Davenport-Heilbronn theorem on the mean size of the 3-part of the class group without first passing through cubic fields. We also prove a uniform vertical density of Heegner points associated to the $k$-part of the class group high in the cusp of $\\mathcal{F}$, for any odd $k$. This leads to a conjectural negative secondary main term in the mean size of the $k$-part of the class group, refining the prediction of the Cohen-Lenstra heuristic.",
      "comment": "Updated references",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2016-05-17T02:07:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "class group",
      "imaginary quadratic field",
      "heegner points",
      "average equidistribution",
      "conjectural negative secondary main term"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.1458H"
    }
  }
}