{
  "id": "1605.07553",
  "version": "v1",
  "published": "2016-05-24T17:35:01.000Z",
  "updated": "2016-05-24T17:35:01.000Z",
  "title": "Bounds on short character sums and L-functions for characters with a smooth modulus",
  "authors": [
    "William Banks",
    "Igor Shparlinski"
  ],
  "comment": "14 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We combine the classical idea of Postnikov (1956) with a method of Korobov (1974) for estimating double Weyl sums to derive new bounds on short character sums when the modulus $q$ has a small core $\\mathfrak{q}_\\sharp=\\prod_{p\\mid q}p$. Using this estimate, we improve certain bounds of Gallagher (1972) and Iwaniec (1974) for the corresponding $L$-functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-24T17:35:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11L40",
      "11L26",
      "11M06",
      "11M20"
    ],
    "keywords": [
      "short character sums",
      "smooth modulus",
      "l-functions",
      "estimating double weyl sums",
      "small core"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}