The Exceptional Zero Conjecture for Symmetric Powers of CM Modular Forms: the Ordinary Case.

We prove the exceptional zero conjecture for the symmetric powers of complex multiplication cuspidal eigenforms at ordinary primes. In other words, we determine the trivial zeros of the associated p-adic L-functions, compute the L-invariants, and show that they agree with Greenberg’s L-invariants. In the appendix, we prove a functional equation for some of the p-adic L-functions we construct. [ABSTRACT FROM AUTHOR]