On entire functions which share one value CM with their first derivative
type: Item
instance of: scholarly article
title: On entire functions which share one value CM with their first derivative
zbMATH Open document ID: 0861.30032
DOI: 10.1007/BF03322176
author: Rainer Brück
published in: Results in Mathematics
publication date: 1996-10-10T00:00:00Z
review text: This article is devoted to considering the following conjecture: Let \(f\) be a nonconstant entire function of finite noninteger iterated order \[ \rho_1(f) = \lim\sup_{r\to \infty} \log \log T(r,f)/ \log r. \] If \(f\), \(f'\) share a value \(a\in \mathbb{C}\) counting multiplicity, then for a constant \(c\in \mathbb{C} \backslash \{0\}\), \((f'-a)/(f-a)=c\). Now, two theorems related to this conjecture will be proved: (1) The conjecture is true for \(a= 0\). (2) If \(f\) is nonconstant entire, \(N(r,{1 \over f'}) = S(r,f)\) ad \(f\), \(f'\) share \(a=1\) counting multiplicity, then for a constant \(c\in \mathbb{C} \backslash \{0\}\), \((f'-1)/(f-1) =c\). Observe that the growth condition has been dropped in (2).
reviewed by: Ilpo Laine
Mathematics Subject Classification ID: 30D35
zbMATH DE Number: 933252
MaRDI profile type: Publication
cites work: Meromorphic functions that share finite values with their derivative
cites work: Q3995409
cites work: Meromorphe Funktionen, die mit ihrer Ableitung Werte teilen
description: scientific article; zbMATH DE number 933252