{
  "id": "1807.08527",
  "version": "v1",
  "published": "2018-07-23T10:59:55.000Z",
  "updated": "2018-07-23T10:59:55.000Z",
  "title": "On the asymptotics of a cotangent sum related to the Estermann zeta function",
  "authors": [
    "George Fikioris"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "The sum $c_0(1/k)=-\\sum_{m=1}^{k-1}(m/k)\\cot(m{\\pi}/k)$ is related to the Estermann zeta function. A recent paper computes the first two terms of the large-$k$ asymptotic expansion of $c_0(1/k)$. Using the Poisson summation formula for finite sums, we find three additional terms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-23T10:59:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "estermann zeta function",
      "cotangent sum",
      "poisson summation formula",
      "additional terms",
      "finite sums"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}