{
  "id": "math/9811185",
  "version": "v1",
  "published": "1998-11-01T00:00:00.000Z",
  "updated": "1998-11-01T00:00:00.000Z",
  "title": "The polynomial X^2+Y^4 captures its primes",
  "authors": [
    "John Friedlander",
    "Henryk Iwaniec"
  ],
  "comment": "96 pages, published version, abstract added in migration",
  "journal": "Ann. of Math. (2) 148 (1998), no. 3, 945-1040",
  "categories": [
    "math.NT"
  ],
  "abstract": "This article proves that there are infinitely many primes of the form a^2 + b^4, in fact getting the asymptotic formula. The main result is that \\sum_{a^2 + b^4\\le x} \\Lambda(a^2 + b^4) = 4\\pi^{-1}\\kappa x^{3/4} (1 + O(\\log\\log x / \\log x)) where a, b run over positive integers and \\kappa = \\int^1_0 (1 - t^4)^{1/2} dt = \\Gamma(1/4)^2 /6\\sqrt{2\\pi}. Here of course, \\Lambda denotes the von Mangoldt function and \\Gamma the Euler gamma function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-11-01T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "polynomial",
      "euler gamma function",
      "von mangoldt function",
      "asymptotic formula",
      "main result"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Princeton University and the Institute for Advanced Study",
      "journal": "Ann. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 96,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math.....11185F"
    }
  }
}