{
  "id": "1704.00619",
  "version": "v1",
  "published": "2017-04-03T14:31:46.000Z",
  "updated": "2017-04-03T14:31:46.000Z",
  "title": "A note on automorphic L-Invariants",
  "authors": [
    "Lennart Gehrmann"
  ],
  "comment": "14 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We study the behaviour of automorphic L-Invariants associated to cuspidal representations of GL(2) of cohomological weight 0 under abelian base change and Jacquet-Langlands lifts to totally definite quaternion algebras. Under a standard non-vanishing hypothesis on automorphic L-functions and some technical restrictions on the automorphic representation and the base field we get a simple proof of the equality of automorphic and arithmetic L-invariants. This together with Spiess' results on p-adic L-functions yields a new proof of the exceptional zero conjecture for modular elliptic curves - at least, up to sign.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-03T14:31:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "automorphic l-invariants",
      "modular elliptic curves",
      "exceptional zero conjecture",
      "abelian base change",
      "p-adic l-functions yields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}