{
  "id": "1411.2360",
  "version": "v1",
  "published": "2014-11-10T09:30:20.000Z",
  "updated": "2014-11-10T09:30:20.000Z",
  "title": "On the distribution of squarefree integers in arithmetic progressions",
  "authors": [
    "Pierre Le Boudec"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We investigate the error term of the asymptotic formula for the number of squarefree integers up to some bound, and lying in some arithmetic progression a (mod q). In particular, we prove an upper bound for its variance as a varies over $(\\mathbb{Z}/q\\mathbb{Z})^{\\times}$ which considerably improves upon earlier work of Blomer.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-10T09:30:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N37",
      "11N69"
    ],
    "keywords": [
      "squarefree integers",
      "arithmetic progression",
      "distribution",
      "upper bound",
      "asymptotic formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.2360L"
    }
  }
}