Geodesic
$p$-adic L-functions of automorphic forms and exceptional zeros
Documenta mathematica, Tome 21 (2016), pp. 689-734.

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

Summary: We construct $p$-adic L-functions for automorphic representations of $\GL$_2 of a number field $F$ , and show that the corresponding $p$-adic L-function of a modular elliptic curve $E$ over $F$ has an extra zero at the central point for each prime above $p$ at which $E$ has split multiplicative reduction, a part of the exceptional zero conjecture.
Classification : 11F41, 11F67, 11F70, 11G40
Keywords: p-adic L-function, automorphic forms, exceptional zero conjecture, Mazur-Tate-teitelbaum conjecture 
@article{DOCMA_2016__21__a25,
     author = {Deppe, Holger},
     title = {$p$-adic {L-functions} of automorphic forms and exceptional zeros},
     journal = {Documenta mathematica},
     pages = {689--734},
     publisher = {mathdoc},
     volume = {21},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2016__21__a25/}
}
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Deppe, Holger. $p$-adic L-functions of automorphic forms and exceptional zeros. Documenta mathematica, Tome 21 (2016), pp. 689-734. http://geodesic.mathdoc.fr/item/DOCMA_2016__21__a25/