{
  "id": "1708.09483",
  "version": "v1",
  "published": "2017-08-30T21:43:39.000Z",
  "updated": "2017-08-30T21:43:39.000Z",
  "title": "A question proposed by K. Mahler on exceptional sets of transcendental functions with integer coefficients: solution of a Mahler's problem",
  "authors": [
    "Diego Marques",
    "Carlos Gustavo Moreira"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we shall prove that any subset of $\\overline{\\mathbb Q}\\cap B(0,1)$, which is closed under complex conjugation and which contains the element $0$, is the exceptional set of uncountably many transcendental functions, analytic in the unit ball, with integer coefficients. This solves a strong version of an old question proposed by K. Mahler (1976).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-30T21:43:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11Jxx",
      "30Dxx"
    ],
    "keywords": [
      "exceptional set",
      "transcendental functions",
      "integer coefficients",
      "mahlers problem",
      "old question"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}