Geodesic
Functoriality of Automorphic $\mathrm{L}$-Invariants and Applications
Documenta mathematica, Tome 24 (2019), pp. 1225-1243
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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.
DOI : 10.4171/dm/703
Classification : 11F41, 11F67, 11F75, 11F85, 11G05
Mots-clés : modular forms, automorphic representations, p-adic periods 
@article{10_4171_dm_703,
     author = {Lennart Gehrmann},
     title = {Functoriality of {Automorphic} $\mathrm{L}${-Invariants} and {Applications}},
     journal = {Documenta mathematica},
     pages = {1225--1243},
     year = {2019},
     volume = {24},
     doi = {10.4171/dm/703},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/703/}
}
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Lennart Gehrmann. Functoriality of Automorphic $\mathrm{L}$-Invariants and Applications. Documenta mathematica, Tome 24 (2019), pp. 1225-1243. doi: 10.4171/dm/703

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