The Behaviour of Rigid Analytic Functions around Orbits of Elements of ${\mathbb{C}}_p$

Abstract

Given a prime number $p$ and the Galois orbit $O(x)$ of an element $x$ of ${\mathbb{C}}_p$, the topological completion of the algebraic closure of the field of $p$-adic numbers, we study the behavior of rigid analytic functions around orbits of elements of ${\mathbb{C}}_p$.