A sharp form of Nevanlinna's Second Main Theorem of several complex variables
type: Item
instance of: scholarly article
title: A sharp form of Nevanlinna's Second Main Theorem of several complex variables
zbMATH Open document ID: 0843.32001
DOI: 10.1007/BF02621859
author: Zhuan Ye
published in: Mathematische Zeitschrift
publication date: 1996-03-21T00:00:00Z
full work available at URL: https://eudml.org/doc/174877
review text: Recently, motivated by relations between Nevanlinna theory and the theory of heights in number theory, one has started finding precise error terms of the Second Main Theorem in Nevanlinna theory. In this paper, we first extend the best logarithmic derivative lemma from one complex variable to several complex variables. Then we prove a sharp form of the Second Main Theorem for meromorphic functions of several complex variables by using the logarithmic derivative lemma. Moreover, we obtain the best upper bound of error terms of the Second Main Theorem for meromorphic functions of finite order. Finally, we show a sharp estimate on upper bound of Nevanlinna secondary deficiency.
Mathematics Subject Classification ID: 32A22
Mathematics Subject Classification ID: 32A30
Mathematics Subject Classification ID: 30D35
Mathematics Subject Classification ID: 32A20
zbMATH DE Number: 838481
zbMATH Keywords: Second Main Theorem
zbMATH Keywords: Nevanlinna theory
zbMATH Keywords: meromorphic functions
zbMATH Keywords: logarithmic derivative
zbMATH Keywords: best upper bound
zbMATH Keywords: error terms
zbMATH Keywords: Nevanlinna secondary deficiency
MaRDI profile type: Publication
cites work: Q3963334
cites work: Q4332775
cites work: The minimum modulus of integral functions of order one
cites work: A sharp form of Nevanlinna's second fundamental theorem
cites work: The error term in Nevanlinna theory
cites work: Topics in Nevanlinna theory
cites work: A Sharp Form of the Lemma on the Logarithmic Derivative
cites work: Q5597066
cites work: Q3958740
cites work: Q4866956
cites work: The lemma of the logarithmic derivative in several complex variables
cites work: On the Second Main Theorem of Nevanlinna Theory
cites work: Second Main Theorem of Nevalinna Theory for Nonequidimensional Meromorphic Maps
cites work: On Nevanlinna's error terms
cites work: The Error Term of Holomorphic Mappings in Nevanlinna Theory
cites work: Q4698996
description: scientific article; zbMATH DE number 838481