{
  "id": "2404.01047",
  "version": "v2",
  "published": "2024-04-01T11:06:15.000Z",
  "updated": "2024-04-04T13:35:42.000Z",
  "title": "On the distribution of $αp+β$ modulo one for primes of type $p=ar^2+1$",
  "authors": [
    "T. Todorova"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "A classical problem in analytic number theory is to study the distribution of fractional part $\\alpha p+\\beta$ modulo 1, where $\\alpha$ is irrational and $p$ runs over the set of primes. We consider the subsequence generated by the primes $p$ such that $p=ar^2+1$ and prove that its distribution has a similar property.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-04-04T13:35:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "distribution",
      "analytic number theory",
      "fractional part",
      "similar property",
      "irrational"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}