{
  "id": "1905.01678",
  "version": "v1",
  "published": "2019-05-05T13:13:53.000Z",
  "updated": "2019-05-05T13:13:53.000Z",
  "title": "Simultaneous approximation to values of the exponential function over the adeles",
  "authors": [
    "Damien Roy"
  ],
  "comment": "33 pages, 1 figure; a French version was posted earlier",
  "categories": [
    "math.NT"
  ],
  "abstract": "We show that Hermite's approximations to values of the exponential function at given algebraic numbers are nearly optimal when considered from an adelic perspective. We achieve this by taking into account the ratio of these values whenever they make sense in the various completions (Archimedean or $p$-adic) of a number field containing these algebraic numbers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-05T13:13:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J13",
      "11J61",
      "11J82",
      "11H06"
    ],
    "keywords": [
      "exponential function",
      "simultaneous approximation",
      "algebraic numbers",
      "hermites approximations",
      "completions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}