{
  "id": "2212.05825",
  "version": "v1",
  "published": "2022-12-12T10:50:04.000Z",
  "updated": "2022-12-12T10:50:04.000Z",
  "title": "Rationality of twist representation zeta functions of compact $p$-adic analytic groups",
  "authors": [
    "Alexander Stasinski",
    "Michele Zordan"
  ],
  "comment": "Second part of arXiv:2007.10694",
  "categories": [
    "math.GR"
  ],
  "abstract": "We prove that for any twist rigid compact $p$-adic analytic group $G$, its twist representation zeta function is a finite sum of terms $n_{i}^{-s}f_{i}(p^{-s})$, where $n_{i}$ are natural numbers and $f_{i}(t)\\in\\mathbb{Q}(t)$ are rational functions. Meromorphic continuation and rationality of the abscissa of the zeta function follow as corollaries. If $G$ is moreover a pro-$p$ group, we prove that its twist representation zeta function is rational in $p^{-s}$. To establish these results we develop a Clifford theory for twist isoclasses of representations, including a new cohomological invariant of a twist isoclass. Second part of arXiv:2007.10694.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-12T10:50:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "twist representation zeta function",
      "adic analytic group",
      "rationality",
      "twist isoclass",
      "twist rigid compact"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}