L-Invariants, p-Adic Heights, and Factorization of p-Adic L-Functions

We continue with our study of the noncritical exceptional zeros of Katz' p-adic L-functions attached to a CM field K, following two threads. In the 1st thread, we redefine our (group-ring-valued) L-invariant associated with each Z(p)-extension K-Gamma of K in terms of p-adic height pairings and interpolate them as K-Gamma varies to a universal (multivariate) group-ring-valued L-invariant. In the 2nd thread, we use our results to study the exceptional zeros of the Rankin-Selberg p-adic L-functions at noncritical specializations of the self-products of nearly ordinary CM families, via the factorization statements we establish. The factorization theorems are extensions of the results due to Greenberg and Palvannan.