# Generating sets of Galois equivariant Krasner analytic functions

### Victor Alexandru

University of Bucharest, Romania### Marian Vâjâitu

Romanian Academy, Bucharest, Romania### Alexandru Zaharescu

Romanian Academy, Bucharest, Romania, and University of Illinois at Urbana-Champaign, USA

## 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 $\mathbb C_p$.

## Cite this article

Victor Alexandru, Marian Vâjâitu, Alexandru Zaharescu, Generating sets of Galois equivariant Krasner analytic functions. Rend. Sem. Mat. Univ. Padova 141 (2019), pp. 195–208

DOI 10.4171/RSMUP/22