Geodesic
Functoriality of Automorphic $\mathrm{L}$-Invariants and Applications
Documenta mathematica, Tome 24 (2019), pp. 1225-1243.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We study the behaviour of automorphic $\mathrm{L}$-invariants associated to cuspidal representations of $\mathrm{GL}(2)$ 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 $\mathrm{L}$-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 $\mathrm{L}$-invariants. This together with Spieß' results on $p$-adic $\mathrm{L}$-functions yields a new proof of the exceptional zero conjecture for modular elliptic curves -- at least, up to sign.
Classification : 11F41, 11F67, 11F75, 11F85, 11G05
Keywords: \(p\)-adic periods, modular forms, automorphic representations 
@article{DOCMA_2019__24__a32,
     author = {Gehrmann, Lennart},
     title = {Functoriality of {Automorphic} {\(\mathrm{L}\)-Invariants} and {Applications}},
     journal = {Documenta mathematica},
     pages = {1225--1243},
     publisher = {mathdoc},
     volume = {24},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2019__24__a32/}
}
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Gehrmann, Lennart. Functoriality of Automorphic \(\mathrm{L}\)-Invariants and Applications. Documenta mathematica, Tome 24 (2019), pp. 1225-1243. http://geodesic.mathdoc.fr/item/DOCMA_2019__24__a32/