{
  "id": "1710.06990",
  "version": "v1",
  "published": "2017-10-19T02:42:02.000Z",
  "updated": "2017-10-19T02:42:02.000Z",
  "title": "On meromorphic solutions of functional equations of Fermat type",
  "authors": [
    "Pei-chu Hu",
    "Qiong Wang"
  ],
  "comment": "15pages, conference",
  "categories": [
    "math.CV"
  ],
  "abstract": "Take complex numbers $a_j,b_j$, $(j=0,1,2)$ such that $c\\neq0$ and {\\rm rank} ( {ccc} a_{0} & a_{1} & a_{2} b_{0} & b_{1} & b_{2} )=2. We show that if the following functional equation of Fermat type \\left\\{a_{0}f(z)+a_{1}f(z+c)+a_{2}f'(z)\\right\\}^3+\\left\\{b_{0}f(z)+b_{1}f(z+c)+b_{2}f'(z)\\right\\}^3=e^{\\alpha z+\\beta} has meromorphic solutions of finite order, then it has only entire solutions of the form $f(z)=Ae^{\\frac{\\alpha z+\\beta}{3}}+Ce^{Dz},$ which generalizes the results in {19} and {14}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-19T02:42:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "39B32",
      "34M05",
      "30D30"
    ],
    "keywords": [
      "fermat type",
      "meromorphic solutions",
      "functional equation",
      "entire solutions",
      "finite order"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}