Functoriality of Automorphic L\mathrm{L}-Invariants and Applications

  • Lennart Gehrmann

    Fakultät für Mathematik, Universität Duisburg-Essen, Thea-Leymann-Straße 9, 45127 Essen, Germany
Functoriality of Automorphic $\mathrm{L}$-Invariants and Applications cover
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We study the behaviour of automorphic L\mathrm{L}-invariants associated to cuspidal representations of GL(2)\mathrm{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\mathrm{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\mathrm{L}-invariants. This together with Spieß' results on pp-adic L\mathrm{L}-functions yields a new proof of the exceptional zero conjecture for modular elliptic curves -- at least, up to sign.

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Lennart Gehrmann, Functoriality of Automorphic L\mathrm{L}-Invariants and Applications. Doc. Math. 24 (2019), pp. 1225–1243

DOI 10.4171/DM/703