{
  "id": "2301.06495",
  "version": "v1",
  "published": "2023-01-16T16:10:14.000Z",
  "updated": "2023-01-16T16:10:14.000Z",
  "title": "Transcendence of some infinite series",
  "authors": [
    "Fedoua Sghiouer",
    "Kacem Belhroukia",
    "Ali Kacha"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In the present paper and as an application of Roth's theorem concerning the rational approximation of algebraic numbers, we give a sufficient condition that will assure us that a series of positive rational terms is a transcendental number. With the same conditions, we establish a transcendental measure of $ \\sum_{n = 1}^{\\infty} 1/a_n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-16T16:10:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "infinite series",
      "transcendence",
      "transcendental measure",
      "transcendental number",
      "rational approximation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}