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

2012; Oxford University Press; Volume: 2013; Issue: 16 Linguagem: Inglês

10.1093/imrn/rns161

1687-0247

Robert Harron,

Analytic Number Theory Research

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.