{
  "id": "2405.18576",
  "version": "v1",
  "published": "2024-05-28T20:49:08.000Z",
  "updated": "2024-05-28T20:49:08.000Z",
  "title": "Density versions of the binary Goldbach problem",
  "authors": [
    "Ali Alsetri",
    "Xuancheng Shao"
  ],
  "comment": "9 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\delta > 1/2$. We prove that if $A$ is a subset of the primes such that the relative density of $A$ in every reduced residue class is at least $\\delta$, then almost all even integers can be written as the sum of two primes in $A$. The constant $1/2$ in the statement is best possible. Moreover we give an example to show that for any $\\varepsilon > 0$ there exists a subset of the primes with relative density at least $1 - \\varepsilon$ such that $A+A$ misses a positive proportion of even integers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-28T20:49:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "binary goldbach problem",
      "density versions",
      "relative density",
      "reduced residue class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}