Geodesic
$p$-adic L-functions of automorphic forms and exceptional zeros
Documenta mathematica, Tome 21 (2016), pp. 689-734
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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.
DOI : 10.4171/dm/543
Classification : 11F41, 11F67, 11F70, 11G40
Mots-clés : p-adic L-function, automorphic forms, exceptional zero conjecture, Mazur-Tate-teitelbaum conjecture 
@article{10_4171_dm_543,
     author = {Holger Deppe},
     title = {$p$-adic {L-functions} of automorphic forms and exceptional zeros},
     journal = {Documenta mathematica},
     pages = {689--734},
     year = {2016},
     volume = {21},
     doi = {10.4171/dm/543},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/543/}
}
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Holger Deppe. $p$-adic L-functions of automorphic forms and exceptional zeros. Documenta mathematica, Tome 21 (2016), pp. 689-734. doi: 10.4171/dm/543

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