{
  "id": "2105.11699",
  "version": "v1",
  "published": "2021-05-25T06:45:44.000Z",
  "updated": "2021-05-25T06:45:44.000Z",
  "title": "The Average Size of Ramanujan Sums over Cubic Number Fields",
  "authors": [
    "Jing Ma",
    "Huayan Sun",
    "Wenguang Zhai"
  ],
  "comment": "17 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let K be a cubic number field. In this paper, we study the Ramanujan sums c_{J}(I), where I and J are integral ideals in O_{K}. The asymptotic behaviour of sums of c_{J}(I) over both I and J is investigated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-25T06:45:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N37",
      "11L03",
      "11R16"
    ],
    "keywords": [
      "cubic number field",
      "ramanujan sums",
      "average size",
      "integral ideals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}