{
  "id": "2205.00419",
  "version": "v1",
  "published": "2022-05-01T08:17:31.000Z",
  "updated": "2022-05-01T08:17:31.000Z",
  "title": "Pro-isomorphic zeta functions of some $D^\\ast$ Lie lattices of even rank",
  "authors": [
    "Yifat Moadim-Lesimcha",
    "Michael M. Schein"
  ],
  "comment": "11 pages, comments welcome",
  "categories": [
    "math.GR",
    "math.RA"
  ],
  "abstract": "We compute the local pro-isomorphic zeta functions at all but finitely many primes for a certain family of class-two-nilpotent Lie lattices of even rank, parametrized by irreducible non-linear polynomials $f(x) \\in \\mathbb{Z} [x]$, that corresponds to a family of groups introduced by Grunewald and Segal. The result is expressed in terms of a combinatorially defined family of rational functions satisfying a functional equation upon inversion of the variables.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-01T08:17:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "local pro-isomorphic zeta functions",
      "class-two-nilpotent lie lattices",
      "functional equation",
      "irreducible non-linear polynomials",
      "rational functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}