{
  "id": "2408.01314",
  "version": "v1",
  "published": "2024-08-02T15:05:50.000Z",
  "updated": "2024-08-02T15:05:50.000Z",
  "title": "Diophantine Approximation with Piatetski-Shapiro Primes",
  "authors": [
    "Stephan Baier",
    "Habibur Rahaman"
  ],
  "comment": "12 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove that for every irrational number $\\alpha$, real number $c$ satisfying $1<c<9/8$ and positive real number $\\theta$ satisfying $\\theta<(9/c-8)/10$, there exist infinitely many primes of the form $p=\\left[n^c\\right]$ with $n\\in \\mathbb{N}$ such that $||\\alpha p||<p^{-\\theta}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-02T15:05:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J25",
      "11J54",
      "11J71",
      "11L07",
      "11L20",
      "11N36"
    ],
    "keywords": [
      "piatetski-shapiro primes",
      "diophantine approximation",
      "positive real number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}