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Let A be a modular elliptic curve over a totally real field F, and let E/F bea totally imaginary quadratic extension. In the event of exceptional zerophenomenon, we prove a formula for the derivative of the multivariableanticyclotomic p-adic L-function attached to (A,E), in terms of the Hasse-WeilL-function and certain p-adic periods attached to the respective automorphicforms. Our methods are based on a new construction of the anticyclotomic p-adicL-function by means of the corresponding automorphic representation.

Anticyclotomic p-adic l-functions and the exceptional zero phenomenon