{
  "id": "1010.3781",
  "version": "v1",
  "published": "2010-10-19T02:40:00.000Z",
  "updated": "2010-10-19T02:40:00.000Z",
  "title": "On the change of root numbers under twisting and applications",
  "authors": [
    "Ariel Pacetti"
  ],
  "comment": "15 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "The purpose of this article is to show how the root number of a modular form changes by twisting in terms of the local Weil-Deligne representation at each prime ideal. As an application, we show how one can for each odd prime $p$, determine whether a modular form (or a Hilbert modular form) with trivial nebentypus is Steinberg, Principal Series or Supercuspidal at $p$ by analyzing the change of sign under a suitable twist. We also explain the case $p=2$, where twisting is not enough in general.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-10-19T02:40:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F70"
    ],
    "keywords": [
      "root number",
      "application",
      "local weil-deligne representation",
      "modular form changes",
      "hilbert modular form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.3781P"
    }
  }
}