{
  "id": "1404.2699",
  "version": "v1",
  "published": "2014-04-10T05:38:07.000Z",
  "updated": "2014-04-10T05:38:07.000Z",
  "title": "Towards the (ir)rationality of values of Dirichlet series",
  "authors": [
    "Michael Coons",
    "Daniel Sutherland"
  ],
  "comment": "9 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We show that if $F(s)$ is a nondegenerate ordinary Dirichlet series with nonnegative coefficients and $F(k)$ is a rational number for all large enough positive integers $k$, then the denominators of those rational numbers are unbounded. In particular, our result holds for the Riemann zeta function over any arithmetic progression. These results are derived via upper bounds on associated Hankel determinants.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-10T05:38:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J72",
      "11C20",
      "15B05"
    ],
    "keywords": [
      "rational number",
      "rationality",
      "nondegenerate ordinary dirichlet series",
      "riemann zeta function",
      "result holds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.2699C"
    }
  }
}