{
  "id": "1803.02970",
  "version": "v1",
  "published": "2018-03-08T05:18:12.000Z",
  "updated": "2018-03-08T05:18:12.000Z",
  "title": "Eigenvalues of Matrices whose Elements are Ramanujan Sums or Kloosterman Sums",
  "authors": [
    "Noboru Ushiroya"
  ],
  "comment": "22 pages",
  "journal": "Journal of Integer Sequences, Vol. 21 (2018) Article 18.2.6",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $c_q(n)$ be the Ramanujan sums and let $S(m,n;q)$ be the Kloosterman sums. We study the eigenvalues of $q \\times q$ matrices whose $(m,n)$ entry is $c_q (m-n)$ or $S(m,n;q)$ where $q$ is a fixed positive integer. We also study the eigenvalues of matrices whose entries are sums of Ramanujan sums or sums of Kloosterman sums.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-08T05:18:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "kloosterman sums",
      "ramanujan sums",
      "eigenvalues"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}