{
  "id": "1208.2344",
  "version": "v3",
  "published": "2012-08-11T13:51:20.000Z",
  "updated": "2012-11-06T19:50:30.000Z",
  "title": "Some new inequalities in additive combinatorics",
  "authors": [
    "I. D. Shkredov"
  ],
  "comment": "39 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "In the paper we find new inequalities involving the intersections $A\\cap (A-x)$ of shifts of some subset $A$ from an abelian group. We apply the inequalities to obtain new upper bounds for the additive energy of multiplicative subgroups and convex sets and also a series another results on the connection of the additive energy and so--called higher moments of convolutions. Besides we prove new theorems on multiplicative subgroups concerning lower bounds for its doubling constants, sharp lower bound for the cardinality of sumset of a multiplicative subgroup and its subprogression and another results.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-11-06T19:50:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "additive combinatorics",
      "inequalities",
      "additive energy",
      "sharp lower bound",
      "multiplicative subgroups concerning lower bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.2344S"
    }
  }
}