Uniquely factorizable entire functions (Q923754)

The author proves some results on unique factorization. Let f(z) be a transcendental entire function \(n\geq 3\) a prime number. Then \((f(\omega)- a\omega)\circ z^ n\) and \(((\omega -a)f(\omega))\circ z^ n\) are uniquely factorizable for each complex number a, except for a countable set. Furthermore if f(z) is prime and f(z) has infnitely many zeros such that almost all zeros are in \(| \arg z-\pi | <\omega\) \((0<\omega <\frac{\pi}{2})\), then \(f^ n\) is uniquely factorizable.