{
  "id": "2401.05052",
  "version": "v1",
  "published": "2024-01-10T10:22:06.000Z",
  "updated": "2024-01-10T10:22:06.000Z",
  "title": "Moments of Averages of Ramanujan Sums over Number Fields",
  "authors": [
    "Sneha Chaubey",
    "Shivani Goel"
  ],
  "comment": "15 pages. arXiv admin note: text overlap with arXiv:2109.09398",
  "categories": [
    "math.NT"
  ],
  "abstract": "Assuming the generalized Lindel\\\"of hypothesis, we provide asymptotic formulas for the mean values of the first and second moments of Ramanujan sums over any number field. Additionally, unconditionally, we estimate the second moment of Ramanujan sums over cyclotomic number fields.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-10T10:22:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06",
      "11R18",
      "11N37"
    ],
    "keywords": [
      "ramanujan sums",
      "second moment",
      "cyclotomic number fields",
      "mean values",
      "asymptotic formulas"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}