Let F be a totally real field and let E/F be a CM quadratic extension. We construct a p-adic L-function attached to Hida families for the group GL2/F× ResE/FGL1. It is characterised by an exact interpolation property for critical Rankin-Selberg L-values, at classical points corresponding to representations π X with the weights of X smaller than the weights of π. Our p-adic L-function agrees with previous results of Hida when E F splits above p or F = Q, and it is new otherwise. Exploring a method that should bear further fruits, we build it as a ratio of families of global and localWaldspurger zeta integrals, the latter constructed using the local Langlands correspondence in families. In an appendix of possibly independent recreational interest, we give a reality-TV-inspired proof of an identity concerning double factorials.
ASJC Scopus subject areas
- Mathematics (all)