{
  "id": "1804.09084",
  "version": "v1",
  "published": "2018-04-24T15:05:38.000Z",
  "updated": "2018-04-24T15:05:38.000Z",
  "title": "A new explicit formula in the additive theory of primes with applications II. The exceptional set in Goldbach's problem",
  "authors": [
    "Janos Pintz"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Improving earlier estimates of several authors we show that the number E(X) of Goldbach exceptional even integers (that is, even integers which cannot be written as the sum of two primesw) below X satisfies tho bound E(X) < X^0.72 for sufficiently large X. In the proof crucial role is played by the explicit formula for the contribution of the major arcs proved in Part I of this series (arXiv:1804.05561).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-24T15:05:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11P32"
    ],
    "keywords": [
      "explicit formula",
      "exceptional set",
      "goldbachs problem",
      "additive theory",
      "applications"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}