{
  "id": "2112.08249",
  "version": "v2",
  "published": "2021-12-15T16:27:58.000Z",
  "updated": "2022-11-07T19:35:59.000Z",
  "title": "New estimates on the size of $(α,2α)$-Furstenberg sets",
  "authors": [
    "Daniel Di Benedetto",
    "Joshua Zahl"
  ],
  "comment": "28 pages, 1 figure. v2: revised based on referee comments; results are unchanged",
  "categories": [
    "math.CA",
    "math.CO",
    "math.MG"
  ],
  "abstract": "We use recent advances on the discretized sum-product problem to obtain new bounds on the Hausdorff dimension of planar $(\\alpha,2\\alpha)$-Fursterberg sets. This provides a quantitative improvement to the $2\\alpha+\\epsilon$ bound of H\\'era-Shmerkin-Yavicoli. In particular, we show that every $1/2$-Furstenberg set has dimension at least $1 + 1/4536$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-11-07T19:35:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "furstenberg set",
      "hausdorff dimension",
      "discretized sum-product problem",
      "fursterberg sets",
      "quantitative improvement"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}