{
  "id": "0811.1362",
  "version": "v1",
  "published": "2008-11-09T21:06:54.000Z",
  "updated": "2008-11-09T21:06:54.000Z",
  "title": "Analytic continuation of Dirichlet series with almost periodic coefficients",
  "authors": [
    "Oliver Knill",
    "John Lesieutre"
  ],
  "comment": "15 pages",
  "categories": [
    "math.CV"
  ],
  "abstract": "We prove that an ordinary Dirichlet series with coefficients a(n)=g(n b) has an abscissa of convergence 0 if g is an odd 1-periodic, real-analytic function and b is Diophantine. We also show that if g is odd and has bounded variation and b is of bounded Diophantine type r>1, then the abscissa of convergence is smaller or equal than 1-1/r. Using a polylogarithm expansion, we prove that if g is odd and real analytic and b is Diophantine, then the ordinary Dirichlet series has an analytic continuation to the entire complex plane.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-11-09T21:06:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M99",
      "30D99",
      "33E20"
    ],
    "keywords": [
      "analytic continuation",
      "periodic coefficients",
      "ordinary dirichlet series",
      "entire complex plane",
      "real-analytic function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0811.1362K"
    }
  }
}