An Elementary Proof of a Weak Exceptional Zero Conjecture

[摘要] In this paper we extend Darmon's theory of ``integration on $uh_pimes uh$''to cusp forms $f$ of higher even weight. This enables us to prove a ``weakexceptional zero conjecture'': that when the $p$-adic $L$-function of $f$ hasan exceptional zero at the central point, the $mathcal{L}$-invariant arising isindependent of a twist by certain Dirichlet characters.

[学科分类] 数学（综合）