{
  "id": "2308.11397",
  "version": "v1",
  "published": "2023-08-22T12:37:59.000Z",
  "updated": "2023-08-22T12:37:59.000Z",
  "title": "Ordering of number fields and distribution of class groups: abelian extensions",
  "authors": [
    "Weitong Wang"
  ],
  "comment": "Any comments are welcome!",
  "categories": [
    "math.NT"
  ],
  "abstract": "When p divides the ordering of Galois group, the distribution of the Sylow p-subgroup of Cl(K) is closely related to the problem of counting fields with certain specifications. Moreover, different orderings of number fields affect the answers of such questions in a nontrivial way. So, in this paper, we set up an invariant of number fields with parameters, and consider field counting problems with specifications while the parameters change as a variable. The case of abelian extensions shows that, roughly speaking, the result of counting abelian fields is a function of the invariant with parameters.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-22T12:37:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "abelian extensions",
      "class groups",
      "distribution",
      "number fields affect",
      "parameters change"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}