<i>p</i>-adic <i>L</i>-functions via local–global interpolation: the case of

Abstract Let F be a totally real field, and let $E/F$ CM quadratic extension. We construct p -adic L -function attached to Hida families for the group $\mathrm {GL}_{2/F}\times \mathrm {Res}_{E/F}\mathrm {GL}_{1}$ . It is characterized by an exact interpolation property critical Rankin–Selberg -values, at classical points corresponding representations $\pi \boxtimes \chi $ with weights of $\chi smaller than Our agrees previous results when splits above or $F=\mathbf {Q}$ , it new otherwise. Exploring method that should bear further fruits, we build as ratio global local Waldspurger zeta integrals, latter constructed using Langlands correspondence in families. In appendix possibly independent recreational interest, give reality-TV-inspired proof identity concerning double factorials.