Multi-variable admissible distributions

The theory of admissible distributions over a weight-space of one-variable was studied by Amice–Vélu and played important roles in the cyclotomic Iwasawa theory of non-ordinary p-adic Galois representations. In this article, we discuss the multi-variable generalization of the theory of admissible distributions over a weight-space of several variables. As an application, we construct a two-variable non-ordinary p-adic L-function which interpolates the special values of Rankin-Selberg L-functions.