{
  "id": "1104.1906",
  "version": "v2",
  "published": "2011-04-11T11:16:43.000Z",
  "updated": "2012-07-17T07:59:59.000Z",
  "title": "Sums of products of Ramanujan sums",
  "authors": [
    "László Tóth"
  ],
  "comment": "13 pages, revised",
  "journal": "Annali dell' Universita di Ferrara, Volume 58, Number 1 (2012), 183-197",
  "doi": "10.1007/s11565-011-0143-3",
  "categories": [
    "math.NT"
  ],
  "abstract": "The Ramanujan sum $c_n(k)$ is defined as the sum of $k$-th powers of the primitive $n$-th roots of unity. We investigate arithmetic functions of $r$ variables defined as certain sums of the products $c_{m_1}(g_1(k))...c_{m_r}(g_r(k))$, where $g_1,..., g_r$ are polynomials with integer coefficients. A modified orthogonality relation of the Ramanujan sums is also derived.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-07-17T07:59:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A25",
      "11A07",
      "11N37"
    ],
    "keywords": [
      "ramanujan sum",
      "th powers",
      "th roots",
      "modified orthogonality relation",
      "integer coefficients"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.1906T"
    }
  }
}