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arXiv · 1704.00619

Functoriality of automorphic L-invariants and applications

Lennart Gehrmann
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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.

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Lennart Gehrmann. 2019-07-17. Functoriality of automorphic L-invariants and applications. https://doi.org/10.25537/dm.2019v24.1225-1243

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