{
  "id": "1805.07967",
  "version": "v1",
  "published": "2018-05-21T10:10:44.000Z",
  "updated": "2018-05-21T10:10:44.000Z",
  "title": "Set-theoretical entropies of Euler's totient function and other number theoretical special functions",
  "authors": [
    "Fatemah Ayatollah Zadeh Shirazi",
    "Reza Yaghmaeian"
  ],
  "comment": "7 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In the following text we show set--theoretical entropy of Euler's totient function and contravariant set--theoretical entropy of Dedekind psi function are zero. Also contravariant set--theoretical entropy of Euler's totient function and set--theoretical entropy of Dedekind psi function are $+\\infty$. We pay attention to some of the other number theoretical special functions too. We continue our studies on Alexandroff topologies induced by Euler's totient function and Dedekind psi function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-21T10:10:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A25",
      "11Y70",
      "33F99"
    ],
    "keywords": [
      "eulers totient function",
      "number theoretical special functions",
      "dedekind psi function",
      "contravariant set-theoretical entropy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}