{
  "id": "2110.13657",
  "version": "v2",
  "published": "2021-10-26T12:56:27.000Z",
  "updated": "2021-11-11T10:47:29.000Z",
  "title": "Riesz capacities of a set due to Dobiński",
  "authors": [
    "Nicola Arcozzi",
    "Nikolaos Chalmoukis"
  ],
  "comment": "7 pages",
  "categories": [
    "math.CA",
    "math.NT"
  ],
  "abstract": "We study the Riesz $(a,p)$-capacity of the so called Dobi\\'nski set. We characterize the values of the parameters $a$ and $p$ for which the $(a,p)$-Riesz capacity of the Dobi\\'nski set is positive. In particular we show that the Dobi\\'nski set has positive logarithmic capacity, thus answering a question of Dayan, Fernand\\'ez and Gonz\\'alez. We approach the problem by considering the dyadic analogues of the Riesz $(a,p)$-capacities which seem to be better adapted to the problem.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2021-11-11T10:47:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "31C20",
      "30C85",
      "31A15",
      "11J83"
    ],
    "keywords": [
      "riesz capacity",
      "dobinski set",
      "positive logarithmic capacity",
      "dyadic analogues",
      "parameters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}