Generating sets of Galois equivariant Krasner analytic functions

Abstract

Given a prime number $p$ and $x$ an element of the Tate field ${\mathbb{C}}_p$, the main goal of the present paper is to provide an explicit generating set, which is given by the trace function of $x$ and all its derivatives, for the ${\mathbb{C}}_p$-Banach algebra of the Galois equivariant Krasner analytic functions defined on the complement in ${\mathbb{P}}^1({\mathbb{C}}_p)$ of the orbit of $x$ with values in ${\mathbb{C}}_p$.