{
  "id": "1507.01340",
  "version": "v1",
  "published": "2015-07-06T07:39:04.000Z",
  "updated": "2015-07-06T07:39:04.000Z",
  "title": "Zeroes of partial sums of the zeta-function",
  "authors": [
    "David J. Platt",
    "Timothy S. Trudgian"
  ],
  "comment": "6 Pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "This article considers the positive integers $N$ for which $\\zeta_{N}(s) = \\sum_{n=1}^{N} n^{-s}$ has zeroes in the half-plane $\\Re(s)>1$. Building on earlier results, we show that there are no zeroes for $1\\leq N\\leq 18$ and for $N=20, 21, 28$. For all other $N$ there are infinitely many zeroes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-06T07:39:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06",
      "11Y35"
    ],
    "keywords": [
      "partial sums",
      "zeta-function",
      "earlier results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150701340P"
    }
  }
}