{
  "id": "2101.09770",
  "version": "v1",
  "published": "2021-01-24T18:47:56.000Z",
  "updated": "2021-01-24T18:47:56.000Z",
  "title": "On multiplicative energy of subsets of varieties",
  "authors": [
    "Ilya D. Shkredov"
  ],
  "comment": "20 pages",
  "categories": [
    "math.CO",
    "math.AG",
    "math.CA",
    "math.NT"
  ],
  "abstract": "We obtain a non--trivial upper bound for the multiplicative energy of any sufficiently large subset of a subvariety of a finite algebraic group. We also find some applications of our results to growth of conjugates classes, estimates of exponential sums and the restriction phenomenon.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-24T18:47:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "multiplicative energy",
      "non-trivial upper bound",
      "finite algebraic group",
      "exponential sums",
      "conjugates classes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}