On the primality of a certain class of entire functions
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.
scientific article; zbMATH DE number 1112724