{
  "id": "1309.7745",
  "version": "v1",
  "published": "2013-09-30T07:49:27.000Z",
  "updated": "2013-09-30T07:49:27.000Z",
  "title": "On the range of $\\sum_{n=1}^\\infty\\pm c_n$",
  "authors": [
    "Xinggang He",
    "Chuntai Liu"
  ],
  "comment": "15 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $\\{c_n\\}_{n=1}^\\infty$ be a sequence of complex numbers. In this paper we answer when the range of $\\sum_{n=1}^\\infty\\pm c_n$ is dense or equal to the complex plane. Some examples are given to explain our results. As its application, we calculate the Hausdorff dimension of the level sets of a Rademacher series with complex coefficients.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-30T07:49:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complex numbers",
      "complex plane",
      "hausdorff dimension",
      "level sets",
      "rademacher series"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.7745H"
    }
  }
}