{
  "id": "1712.00737",
  "version": "v1",
  "published": "2017-12-03T09:42:21.000Z",
  "updated": "2017-12-03T09:42:21.000Z",
  "title": "Explicit formulae for averages of Goldbach representations",
  "authors": [
    "J. Brüdern",
    "J. Kaczorowski",
    "A. Perelli"
  ],
  "comment": "16 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove an explicit formula, analogous to the classical explicit formula for $\\psi(x)$, for the Ces\\`aro-Riesz mean of any order $k>0$ of the number of representations of $n$ as a sum of two primes. Our approach is based on a double Mellin transform and the analytic continuation of certain functions arising therein.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-03T09:42:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11P32",
      "11N05"
    ],
    "keywords": [
      "goldbach representations",
      "classical explicit formula",
      "double mellin transform",
      "analytic continuation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}