An Elementary Proof of a Weak Exceptional Zero Conjecture

Abstract

In this paper we extend Darmon's theory of "integration on H-p x H" to cusp forms f of higher even weight. This enables us to prove a "weak exceptional zero conjecture": that when the p-adic L-function of f has an exceptional zero at the central point, the L-invariant arising is independent of a twist by certain Dirichlet characters.