Exceptional zeros of the $p$-adic $L$-functions of modular forms
(Un exposé de Louisa Orton au séminaire de
théorie des nombres de Chevaleret le 26 avril 2004)
Résumé :
The exceptional zero conjecture (now a theorem of Stevens and
Kato/Kurihara/Tsuji) relates the derivative of the $p$-adic $L$-function
at a point where it has an exceptional zero to the value of the complex
$L$-function. We discuss the application of a method of Henri Darmon to
provide a more elementary proof of a version of this result.