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