Multi-variable admissible distributions

TL;DR

This paper extends the theory of admissible distributions from one-variable to multiple variables and constructs a two-variable non-ordinary p-adic L-function interpolating Rankin-Selberg L-values.

Contribution

It introduces a multi-variable generalization of admissible distributions and applies it to construct a new two-variable p-adic L-function.

Findings

Generalization of admissible distributions to multiple variables

Construction of a two-variable non-ordinary p-adic L-function

Interpolation of Rankin-Selberg L-values

Abstract

The theory of admissible distributions over a weight-space of one-variable was studied by Amice--V\'{e}lu 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.