Deficiencies of composite entire functions
type: Item
instance of: scholarly article
title: Deficiencies of composite entire functions
zbMATH Open document ID: 0966.30024
author: Jianwu Sun
published in: Acta Mathematica Vietnamica
publication date: 2001-08-16T00:00:00Z
review text: Let \(f\) and \(g\) be transcendental entire functions with \(T(r,f) =O(\exp( (\log r)^\alpha))\) and \(T(r,g)=O ((\log r)^\beta)\) where \(0<\alpha<1\), \(\beta>1\) and \(\alpha\beta>1\). Then for any complex numbers \(a\), \(\delta(a,f (g))= \delta(a,f)\) where \(\delta\) is the Nevanlinna deficiency. The theorem generalizes Lemma 3 in \textit{R. Goldstein} [Aequationes Math. 5, 75-84 (1970; Zbl 0204.88002)] who considered the case where \(g\) is a polynomial and \(T(r,f)=O((\log r)^\alpha)\), \(\alpha>1\).
Mathematics Subject Classification ID: 30D35
zbMATH DE Number: 1513023
zbMATH Keywords: Nevanlinna deficiency
reviewed by: Linda R. Sons
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1513023