On p-adic L-functions for GL(2)×GL(3) via pullbacks of Saito–Kurokawa lifts

We build a one-variable p-adic L-function attached to two Hida families of ordinary p-stabilised newforms f, g, interpolating the algebraic part of the central values of the complex L-series when f and g range over the classical specialisations of f, g on a suitable line of the weight space. The construction rests on two major results: an explicit formula for the relevant complex central L-values, and the existence of non-trivial Λ-adic Shintani liftings and Saito–Kurokawa liftings studied in a previous work by the authors. We also illustrate that, under an appropriate sign assumption, this p-adic L-function arises as a factor of a triple product p-adic L-function attached to f, g, and g