On p-adic meromorphic functions
type: Item
instance of: scholarly article
title: On p-adic meromorphic functions
zbMATH Open document ID: 0544.30039
DOI: 10.1215/S0012-7094-83-05033-0
published in: Duke Mathematical Journal
publication date: 1983-01-01T00:00:00Z
review text: Let D denote the open unit disc in \({\mathbb{C}}_ p ({\mathbb{C}}_ p\) denotes the completion of the algebraic closure of \({\mathbb{Q}}_ p)\). For a meromorphic function \(\phi\) on D and \(a\in {\mathbb{C}}_ p\) a certain real function \(T(\phi,a,t)\) of \(t>0\) is introduced which measures the set of zero's of \(\phi\)-a and a growth of the function \(\phi\). This function \(T(\phi,a,t)\) is an analogue of a function in Nevanlinna theory. It is shown that, under the condition that \(T(\phi,a,t)\) is unbounded, the function \(\phi\) is determined by the divisors \(\phi^{-1}(a_ 1)\), \(\phi^{-1}(a_ 2)\), \(\phi^{-1}(a_ 3)\) where \(a_ 1,a_ 2,a_ 3\) are three different points of \({\mathbb{C}}_ p\). We note that \(T(\phi,a,t)\) has no clear meaning in the p-adic case and that the theorem above can easily be proved under the weaker assumption that \(\phi\) is not the quotient of two bounded holomorphic functions on D.
Mathematics Subject Classification ID: 30G06
Mathematics Subject Classification ID: 12J10
Mathematics Subject Classification ID: 12J15
zbMATH DE Number: 3865676
zbMATH Keywords: p-adic functions
zbMATH Keywords: Nevanlinna theory
author: Ha Huy Khoai
MaRDI profile type: Publication
cites work: Q4071850
cites work: Q3853750
cites work: p-adic interpolation and the Mellin-Mazur transform
cites work: Les zéros des fonctions analytiques d'une variable sur un corps valué complet
cites work: p-adic automorphic functions
cites work: Q3415005
full work available at URL: s0012-7094-83-05033-0
OpenAlex ID: W1536374669
description: scientific article; zbMATH DE number 3865676