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.