{
  "id": "0912.1071",
  "version": "v1",
  "published": "2009-12-06T03:03:33.000Z",
  "updated": "2009-12-06T03:03:33.000Z",
  "title": "On character sums over flat numbers",
  "authors": [
    "Ping Xi",
    "Yuan Yi"
  ],
  "comment": "9 pages, with a complete proof of Theorem 3, Section 5. Accepted by J. Number Theory",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $q\\geqslant2$ be an integer, $\\chi$ be any non-principal character mod $q$, and $H=H(q)\\leqslant q.$ In this paper the authors prove some estimates for character sums of the form \\[\\mathcal{W}(\\chi,H;q)=\\sum_{n\\in\\mathscr{F}(H)}\\chi(n),\\] where \\[\\mathscr{F}(H)=\\left\\{n\\in\\mathbb{Z}|(n,q)=1,1\\leqslant n,\\bar{n}\\leqslant q, |n-\\bar{n}|\\leqslant H\\},\\] $\\bar{n}$ is defined by $n\\bar{n}\\equiv1\\pmod q.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-12-06T03:03:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11L40",
      "11L05",
      "11A07"
    ],
    "keywords": [
      "character sums",
      "flat numbers",
      "non-principal character mod"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0912.1071X"
    }
  }
}