{
  "id": "2207.08233",
  "version": "v1",
  "published": "2022-07-17T17:20:44.000Z",
  "updated": "2022-07-17T17:20:44.000Z",
  "title": "Simultaneous $\\mathfrak{p}$-orderings and equidistribution",
  "authors": [
    "Anna Szumowicz"
  ],
  "comment": "14 pages, survey, to appear in conference proceedings \"Algebras and Polynomials: Algebraic, Number Theoretic, and Topological Aspects of Ring Theory\"",
  "categories": [
    "math.NT",
    "math.AC"
  ],
  "abstract": "Let $D$ be a Dedekind domain. Roughly speaking, a simultaneous $\\mathfrak{p}$-ordering is a sequence of elements from $D$ which is equidistributed modulo every power of every prime ideal in $D$ as well as possible. Bhargava asked which subsets of the Dedekind domains admit simultaneous $\\mathfrak{p}$-orderings. We give an overview on the progress in this problem. We also explain how it relates to the theory of integer valued polynomials and list some open problems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-17T17:20:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N25",
      "11K38",
      "13F20",
      "11D57"
    ],
    "keywords": [
      "equidistribution",
      "integer valued polynomials",
      "open problems",
      "prime ideal",
      "dedekind domains admit simultaneous"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}