Anticyclotomic p-adic L-functions and Ichino’s formula
نویسنده
چکیده
We give a new construction of a p-adic L-function L(f,Ξ), for f a holomorphic newform and Ξ an anticyclotomic family of Hecke characters of Q( √ −d). The construction uses Ichino’s triple product formula to express the central values of L(f, ξ, s) in terms of Petersson inner products, and then uses results of Hida to interpolate them. The resulting construction is well-suited for studying what happens when f is replaced by a modular form congruent to it modulo p, and has future applications in the case where f is residually reducible.
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