{
  "id": "1706.04173",
  "version": "v1",
  "published": "2017-06-13T17:29:30.000Z",
  "updated": "2017-06-13T17:29:30.000Z",
  "title": "The Density of Numbers Represented by Diagonal Forms of Large Degree",
  "authors": [
    "Brandon Hanson",
    "Asif Zaman"
  ],
  "comment": "7 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $s \\geq 3$ be a fixed positive integer and $a_1,\\dots,a_s \\in \\mathbb{Z}$ be arbitrary. We show that, on average over $k$, the density of numbers represented by the degree $k$ diagonal form \\[ a_1 x_1^k + \\cdots + a_s x_s^k \\] decays rapidly with respect to $k$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-13T17:29:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "diagonal form",
      "large degree",
      "fixed positive integer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}