{
  "id": "1410.4538",
  "version": "v1",
  "published": "2014-10-16T19:17:25.000Z",
  "updated": "2014-10-16T19:17:25.000Z",
  "title": "Kloosterman sums in residue classes",
  "authors": [
    "Valentin Blomer",
    "Djordje Milićević"
  ],
  "comment": "14 pages, to appear in the Journal of the European Mathematical Society",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove upper bounds for sums of Kloosterman sums against general arithmetic weight functions. In particular, we obtain power cancellation in sums of Kloosterman sums over arithmetic progressions, which is of square-root strength in any fixed primitive congruence class up to bounds towards the Ramanujan conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-16T19:17:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11L05",
      "11F72",
      "11F30",
      "11K36",
      "11L07"
    ],
    "keywords": [
      "kloosterman sums",
      "residue classes",
      "general arithmetic weight functions",
      "upper bounds",
      "ramanujan conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.4538B"
    }
  }
}