{
  "id": "1908.06946",
  "version": "v1",
  "published": "2019-08-19T17:32:18.000Z",
  "updated": "2019-08-19T17:32:18.000Z",
  "title": "Linnik's large sieve and the $L^{1}$ norm of exponential sums",
  "authors": [
    "Emily Eckels",
    "Steven Jin",
    "Andrew Ledoan",
    "Brian Tobin"
  ],
  "comment": "15 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "The method of proof of Balog and Ruzsa and the large sieve of Linnik are used to investigate the behaviour of the $L^{1}$ norm of a wide class of exponential sums over the square-free integers and the primes. Further, a new proof of the lower bound due to Vaughan for the $L^{1}$ norm of an exponential sum with the von Mangoldt $\\Lambda$ function over the primes is furnished. Ramanujan's sum arises naturally in the proof, which also employs Linnik's large sieve.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-19T17:32:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11L03",
      "11L07",
      "11L20",
      "11N36",
      "42A05"
    ],
    "keywords": [
      "exponential sum",
      "employs linniks large sieve",
      "ramanujans sum arises",
      "lower bound",
      "wide class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}