{
  "id": "2312.02628",
  "version": "v1",
  "published": "2023-12-05T10:08:49.000Z",
  "updated": "2023-12-05T10:08:49.000Z",
  "title": "Diophantine approximation with prime denominator in quadratic number fields under GRH",
  "authors": [
    "Stephan Baier",
    "Sourav Das",
    "Esrafil Ali Molla"
  ],
  "comment": "30 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Matom\\\"aki proved that if $\\alpha\\in \\mathbb{R}$ is irrational, then there are infinitely many primes $p$ such that $|\\alpha-a/p|\\le p^{-4/3+\\varepsilon}$ for a suitable integer a. In this paper, we extend this result to all quadratic number fields under the condition that the Grand Riemann Hypothesis holds for their Hecke $L$-functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-05T10:08:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J71",
      "11R11",
      "11R42",
      "11R44"
    ],
    "keywords": [
      "quadratic number fields",
      "prime denominator",
      "diophantine approximation",
      "grand riemann hypothesis holds",
      "irrational"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}