{
  "id": "2103.06481",
  "version": "v1",
  "published": "2021-03-11T05:56:58.000Z",
  "updated": "2021-03-11T05:56:58.000Z",
  "title": "Improved explicit upper bounds for the Cap Set Problem",
  "authors": [
    "Zhi Jiang"
  ],
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "Ellenberg and Gijswijt gave the best known asymptotic upper bound for the cardinality of subsets of $\\mathbb F_q^n$ without 3-term arithmetic progressions. We improve this bound by a factor $\\sqrt{n}$. In the case $q=3$, we also obtain more explicit upper bounds for the Cap Set Problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-11T05:56:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cap set problem",
      "explicit upper bounds",
      "asymptotic upper bound",
      "gijswijt gave",
      "arithmetic progressions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}