Growth and size of the exceptional set in Nevanlinna's second fundamental theorem
type: Item
instance of: scholarly article
title: Growth and size of the exceptional set in Nevanlinna's second fundamental theorem
zbMATH Open document ID: 0921.30022
DOI: 10.1023/A:1004505501177
author: F. Rodríguez
published in: Periodica Mathematica Hungarica
publication date: 1999-09-14T00:00:00Z
review text: Let \(f\) be a transcendental meromorphic function, \(T(r,f)\) its characteristic function and \(S(r,f)\) the error term in Nevanlinna'a second fundamental theorem. It is shown that for every increasing function \(\psi(r)\) such that \(\log\psi (r)=o(r)\) we have \(S(r,f)=o(T(r,f))\) outside an exceptional set \(E\), satisfying \(\int _E\psi (T(r,f)) dr <\infty\). This result makes clear the relationship between the size of the exceptional set and the growth of the characteristic function and implies that for functions of rapid lower growth improved conditions on the size of the exceptional set can be given. A general example of an entire function with a suitable exceptional set is constructed, showing that these results are essentially best possible.
Mathematics Subject Classification ID: 30D35
zbMATH DE Number: 1336270
zbMATH Keywords: Nevanlinna characteristic function
zbMATH Keywords: error term
zbMATH Keywords: exceptional set
reviewed by: A. Klíč
MaRDI profile type: Publication
full work available at URL: a:1004505501177
OpenAlex ID: W1743382121
description: scientific article; zbMATH DE number 1336270