{
  "id": "2109.11111",
  "version": "v1",
  "published": "2021-09-23T02:45:31.000Z",
  "updated": "2021-09-23T02:45:31.000Z",
  "title": "The average size of Ramanujan sums over quadratic number fields(II)",
  "authors": [
    "Wenguang Zhai"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper we study Ramanujan sums $c_{\\bf m}(\\bf n)$, where $ {\\bf m}$ and ${\\bf n}$ are integral ideals in an arbitrary quadratic number field. We give some new results about the asymptotic behavior of sums of $c_{\\bf m}(\\bf n)$ over both $ {\\bf m}$ and $ {\\bf n}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-23T02:45:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N37",
      "11M41"
    ],
    "keywords": [
      "average size",
      "arbitrary quadratic number field",
      "study ramanujan sums",
      "integral ideals",
      "asymptotic behavior"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}