{
  "id": "1710.01091",
  "version": "v1",
  "published": "2017-10-03T11:40:38.000Z",
  "updated": "2017-10-03T11:40:38.000Z",
  "title": "Exponential sums with automatic sequences",
  "authors": [
    "Sary Drappeau",
    "Clemens Müllner"
  ],
  "comment": "14 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We show that automatic sequences are asymptotically orthogonal to periodic exponentials of type $e_q(f(n))$, where $f$ is a rational fraction, in the P\\'olya-Vinogradov range. This applies to Kloosterman sums, and may be used to study solubility of congruence equations over automatic sequences. We obtain this as consequence of a general result, stating that sums over automatic sequences can be bounded effectively in terms of two-point correlation sums over intervals.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-03T11:40:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11L07",
      "11B85",
      "11L05",
      "11L26"
    ],
    "keywords": [
      "automatic sequences",
      "exponential sums",
      "two-point correlation sums",
      "rational fraction",
      "polya-vinogradov range"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}