{
  "id": "2506.18395",
  "version": "v1",
  "published": "2025-06-23T08:30:08.000Z",
  "updated": "2025-06-23T08:30:08.000Z",
  "title": "The second moment of Ramanujan sums",
  "authors": [
    "Hong Ziwei",
    "Zheng Zhiyong"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we analyze $C(x, y)$, the second moment of Ramanujan sums. Assuming the Riemann Hypothesis, we derive an asymptotic formula for $C(x, y)$ with improved error term precision. The key feature of our approach is that it allows $x$ and $y$ to be arbitrarily close.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-06-23T08:30:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ramanujan sums",
      "second moment",
      "error term precision",
      "asymptotic formula",
      "riemann hypothesis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}