We study the behaviour of automorphic -invariants associated to cuspidal representations of 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 -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 -invariants. This together with Spieß' results on -adic -functions yields a new proof of the exceptional zero conjecture for modular elliptic curves -- at least, up to sign.
Cite this article
Lennart Gehrmann, Functoriality of Automorphic -Invariants and Applications. Doc. Math. 24 (2019), pp. 1225–1243DOI 10.4171/DM/703