{
  "id": "2004.07101",
  "version": "v1",
  "published": "2020-04-15T14:11:26.000Z",
  "updated": "2020-04-15T14:11:26.000Z",
  "title": "Transcendental Numbers and the Lambert-Tsallis Function",
  "authors": [
    "J. L. E. da Silva",
    "R. V. Ramos"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "To decide upon the arithmetic nature of some numbers may be a non-trivial problem. Some cases are well know, for example exp(1) and W(1), where W is the Lambert function, are transcendental numbers. The Tsallis q-exponential, e_q (z), and the Lambert-Tsallis W_q (z) function, where q is a real parameter, are, respectively, generalizations of the exponential and Lambert functions. In the present work we use the Gelfond-Schneider theorem in order to show the arithmetic conditions on q and z such that W_q (z) and exp_q (z) are transcendental.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-15T14:11:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "transcendental numbers",
      "lambert-tsallis function",
      "lambert function",
      "arithmetic nature",
      "gelfond-schneider theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}