{
  "id": "2404.01045",
  "version": "v2",
  "published": "2024-04-01T11:01:06.000Z",
  "updated": "2024-04-04T13:29:22.000Z",
  "title": "On the distribution of $αp^2+β$ modulo one for primes $p$ such that $p+2$ has no more two prime divisors",
  "authors": [
    "T. L. Todorova"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "A classical problem in analytic number theory is to study the distribution of fractional part $\\alpha p^k+\\beta,\\,k\\ge 1$ modulo 1, where $\\alpha$ is irrational and $p$ runs over the set of primes. For $k=2$ we consider the subsequence generated by the primes $p$ such that $p+2$ is an almost-prime (the existence of infinitely many such $p$ is another topical result in prime number theory) and prove that its distribution has a similar property.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-04-04T13:29:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "prime divisors",
      "distribution",
      "prime number theory",
      "analytic number theory",
      "similar property"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}