On the primality of a certain class of entire functions
type: Item
instance of: scholarly article
title: On the primality of a certain class of entire functions
zbMATH Open document ID: 0893.30020
published in: Southeast Asian Bulletin of Mathematics
publication date: 1998-08-03T00:00:00Z
review text: A meromorphic function \(F\) has a factorization if \(F=f \circ g\) (1) where \(f\) is meromorphic and \(g\) entire or \(f\) is rational and \(g\) meromorphic. \(F\) is prime if in every factorization (1) either \(f\) is bilinear or \(g\) is linear. Extending a result of F. Gross, C. F. Osgood and C. C. Yang, Nagoya Math. J. 47, 91-99 (1972; Zbl 0239.30032) the authors prove that, given any integer \(k>0\), constant \(c\) with \(0\leq c\leq 1\) and polynomial \(p\), there exists a prime function of order \(k\) such that the deficiency \(\delta (F-p,0)=c\). Further they prove that for \(k>0\), \(c\) in \(0\leq c\leq 1\) as above and any entire function \(h\) with order \(<k\), there exists a right prime entire function \(G\) of order \(k\) such that \(\delta (G-h,0)=c\). The statement that \(G\) is right prime means that in any factorization \(G=f\circ g\) of type (1) with \(f\) transcendental we must have \(g\) linear.
Mathematics Subject Classification ID: 30D35
zbMATH DE Number: 1112724
zbMATH Keywords: prime function
zbMATH Keywords: factorization
author: Liangwen Liao
author: Guo-Dong Song
reviewed by: I. N. Baker
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1112724