{
  "id": "2103.16648",
  "version": "v1",
  "published": "2021-03-30T19:42:31.000Z",
  "updated": "2021-03-30T19:42:31.000Z",
  "title": "Exponential sums with multiplicative coefficients and applications",
  "authors": [
    "Régis de la Bretèche",
    "Andrew Granville"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We show that if an exponential sum with multiplicative coefficients is large then the associated multiplicative function is \"pretentious\". This leads to applications in the circle method, and a natural interpretation of the local-global principle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-30T19:42:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exponential sum",
      "multiplicative coefficients",
      "applications",
      "circle method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}