A characterization of injective holomorphic functions in ultrametric analysis
type: Item
instance of: scholarly article
title: A characterization of injective holomorphic functions in ultrametric analysis
zbMATH Open document ID: 1014.30029
DOI: 10.1016/S1631-073X(02)02501-3
author: Juan Rivera-Letelier
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2003-01-30T00:00:00Z
review text: A criterion is given for the injectivity of holomorphic functions in \(p\)-adic analysis which has been conjectured by A. Escassut and M. C. Sarmant. A counter-example shows that the conjecture is incorrect for bi-analytic elements.The criterion reads as follows: A non constant holomorphic function \(f\) over an analytic subspace over \(\mathbb{C}_p\) is injective if and only if for all \(x \not = y\) \[ \left|\frac{f(x)-f(y)}{x-y}\right|^2= |f'(x) f'(y)|. \]
reviewed by: Klaus Habetha
Mathematics Subject Classification ID: 30G06
Mathematics Subject Classification ID: 12J25
Mathematics Subject Classification ID: 30A99
zbMATH DE Number: 1854327
zbMATH Keywords: ultrametric analysis
zbMATH Keywords: holomorphic function
zbMATH Keywords: \(p\)-adic analysis
MaRDI profile type: Publication
cites work: Q4858391
cites work: Q5286866
cites work: Géométrie analytique rigide et applications. (Ridgid analytic geometry and applications)
cites work: Periodic points, multiplicities, and dynamical units.
cites work: Q3661880
full work available at URL: s1631-073x(02)02501-3
OpenAlex ID: W1987281437
description: scientific article; zbMATH DE number 1854327