Another proof of Stoll's theorem for moving targets
type: Item
instance of: scholarly article
title: Another proof of Stoll's theorem for moving targets
zbMATH Open document ID: 0674.32013
author: Seiki Mori
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1989-01-01T00:00:00Z
review text: In 1929, Nevanlinna asked whether his defect relation remains valid for mutually distinct meromorphic target functions \(g_ 1,...,g_ q\) which grow more slowly than a given meromorphic function f on \({\mathbb{C}}\), that is, \(T(r,g_ j)=o(T(r,f))\) (r\(\to \infty)\), and he proved the conjecture for \(q=3\). In 1986, Steinmetz proved Nevanlinna's conjecture with an elegant short proof. On the other hand, in higher dimension, Stoll proved an analogous defect relation with a defect bound \(n(n+1)\) for holomorphic mappings of \({\mathbb{C}}\) into \({\mathbb{P}}^ n({\mathbb{C}})\) [see \textit{M. Stoll}, Math. Ann. 282, No.2, 185-222 (1988; Zbl 0629.30030)]. In this note, we give a short proof of Stoll's theorem.
Mathematics Subject Classification ID: 32H30
zbMATH DE Number: 4103455
zbMATH Keywords: Nevanlinna theory
zbMATH Keywords: defect relation
zbMATH Keywords: holomorphic mappings
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178227732
OpenAlex ID: W1990216230
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DOI: 10.2748/TMJ/1178227732
description: scientific article; zbMATH DE number 4103455