{
  "id": "1409.3177",
  "version": "v1",
  "published": "2014-09-10T18:30:08.000Z",
  "updated": "2014-09-10T18:30:08.000Z",
  "title": "Averages and moments associated to class numbers of imaginary quadratic fields",
  "authors": [
    "D. R. Heath-Brown",
    "L. B. Pierce"
  ],
  "comment": "25 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "For any odd prime $g$, let $h_g(-d)$ denote the $g$-part of the class number of the imaginary quadratic field $\\mathbb{Q}(\\sqrt{-d})$. Nontrivial pointwise upper bounds are known only for $g=3$; nontrivial upper bounds for averages of $h_g(-d)$ have previously been known only for $g=3,5$. In this paper we prove nontrivial upper bounds for the average of $h_g(-d)$ for all primes $g \\geq 7$, as well as nontrivial upper bounds for certain higher moments for all primes $g \\geq 3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-10T18:30:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R29",
      "11D45"
    ],
    "keywords": [
      "imaginary quadratic field",
      "class number",
      "nontrivial upper bounds",
      "nontrivial pointwise upper bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.3177H"
    }
  }
}