{
  "id": "1802.10278",
  "version": "v1",
  "published": "2018-02-28T06:26:07.000Z",
  "updated": "2018-02-28T06:26:07.000Z",
  "title": "Sign changes of Kloosterman sums and exceptional characters",
  "authors": [
    "Sary Drappeau",
    "James Maynard"
  ],
  "comment": "11 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove that the existence of exceptional real zeroes of Dirichlet $L$-functions would lead to cancellations in the sum $\\sum_{p\\leq x} \\Kl(1, p)$ of Kloosterman sums over primes, and also to sign changes of $\\Kl(1, n)$, where $n$ runs over integers with exactly two prime factors. Our arguments involve a variant of Bombieri's sieve, bounds for twisted sums of Kloosterman sums, and work of Fouvry and Michel on sums of $\\left| \\Kl(1, n)\\right|$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-28T06:26:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11L05",
      "11N36",
      "11N75",
      "11L20",
      "11M20"
    ],
    "keywords": [
      "kloosterman sums",
      "sign changes",
      "exceptional characters",
      "exceptional real zeroes",
      "bombieris sieve"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}