Abstract We construct a p -adic Rankin–Selberg L -function associated to the product of two families of modular forms, where the first is an ordinary (Hida) family, and the second an arbitrary universal-deformation family (without any ordinarity condition at p ). This gives a function on a four-dimensional base space – strictly larger than the ordinary eigenvariety, which is three-dimensional in this case. We prove our p -adic L -function interpolates all critical values of the Rankin–Selberg L -functions for the classical specialisations of our family, and derive a functional equation for our p -adic L -function by applying a recent deep result of Helm and Moss on universal γ-factors.
Hao et al. (Thu,) studied this question.