{
  "id": "2404.04747",
  "version": "v1",
  "published": "2024-04-06T22:13:45.000Z",
  "updated": "2024-04-06T22:13:45.000Z",
  "title": "The $L^1$ mean of the exponential sum of the divisor function",
  "authors": [
    "Tomos Parry"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We give a relatively simple proof that \\[ \\int _0^1\\left |\\sum _{n\\leq x}d(n)e(n\\alpha )\\right |d\\alpha \\asymp \\sqrt x.\\]",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-06T22:13:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exponential sum",
      "divisor function",
      "relatively simple proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}