{
  "id": "2207.08805",
  "version": "v1",
  "published": "2022-07-06T10:24:44.000Z",
  "updated": "2022-07-06T10:24:44.000Z",
  "title": "The Exceptional Set in Goldbach's Problem with Almost Twin Primes",
  "authors": [
    "Lasse Grimmelt",
    "Joni Teräväinen"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We consider the exceptional set in the binary Goldbach problem for sums of two almost twin primes. Our main result is a power-saving bound for the exceptional set in the problem of representing $m=p_1+p_2$ where $p_1+2$ has at most $2$ prime divisors and $p_2+2$ has at most $3$ prime divisors. There are three main ingredients in the proof: a new transference principle like approach for sieves, a combination of the level of distribution estimates of Bombieri--Friedlander--Iwaniec and Maynard with ideas of Drappeau to produce power savings, and a generalisation of the circle method arguments of Montgomery and Vaughan that incorporates sieve weights.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-06T10:24:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11P32",
      "11N35",
      "11N05"
    ],
    "keywords": [
      "exceptional set",
      "twin primes",
      "goldbachs problem",
      "prime divisors",
      "binary goldbach problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}