{
  "id": "1606.00760",
  "version": "v1",
  "published": "2016-06-01T13:00:06.000Z",
  "updated": "2016-06-01T13:00:06.000Z",
  "title": "Enumerating submodules invariant under an endomorphism",
  "authors": [
    "Tobias Rossmann"
  ],
  "comment": "25 pages",
  "categories": [
    "math.NT",
    "math.GR",
    "math.RA"
  ],
  "abstract": "We study zeta functions enumerating submodules invariant under a given endomorphism of a finitely generated module over the ring of ($S$-)integers of a number field. In particular, we compute explicit formulae involving Dedekind zeta functions and establish meromorphic continuation of these zeta functions to the complex plane. As an application, we show that ideal zeta functions associated with nilpotent Lie algebras of maximal class have abscissa of convergence $2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-01T13:00:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M41",
      "15A04",
      "15A21",
      "17B30"
    ],
    "keywords": [
      "endomorphism",
      "zeta functions enumerating submodules invariant",
      "study zeta functions enumerating submodules",
      "dedekind zeta functions",
      "ideal zeta functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}