{
  "id": "2101.05251",
  "version": "v1",
  "published": "2021-01-13T18:32:31.000Z",
  "updated": "2021-01-13T18:32:31.000Z",
  "title": "Simultaneous p-adic Diophantine approximation",
  "authors": [
    "Victor Beresnevich",
    "Jason Levesley",
    "Benjamin Ward"
  ],
  "comment": "26 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "The goal of this paper is to develop the theory of weighted Diophantine approximation of $p$-adic variables. Firstly, we establish complete analogues of Khintchine's theorem and the Jarn\\'ik-Besicovitch theorem for `weighted' simultaneous Diophantine approximation in the $p$-adic case. Secondly, we obtain a lower bound for the Hausdorff dimension of weighted simultaneously approximable points lying on $p$-adic curves. One of the key tools in our proofs is the Mass Transference Principle, including its recent extension due to Wang and Wu. Our result for curves has a natural constraint on the exponents of approximation and, in the case of polynomial curves, complements a theorem of Bugeaud et al, which deals with large exponents.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-13T18:32:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "simultaneous p-adic diophantine approximation",
      "simultaneously approximable points lying",
      "mass transference principle",
      "establish complete analogues",
      "adic curves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}