| In this thesis, we shall prove some results which, in turn, will allow us to solve some factorization problems in a systematic way. Also, we shall utilize new methods from theory of complex analytic sets and local holomorphic dynamics to solve some factorization problems.;In Chapter 5, we shall use results from theory of complex analytic sets to prove certain criteria on the existence of a non-linear entire common right factor of two entire functions. Applying these criteria, we can then prove that if f is an entire function which is pseudo-prime and not of the form H(Q(z)), where H is a periodic entire function and Q is a polynomial, then R(f(z)) is also pseudo-prime for any non-constant rational function R. This result essentially solves a problem of G. D. Song and is a fundamental property of pseudo-prime function. We also give other applications of these criteria to unique factorization problems. In Chapter 6, we consider the unique factorization problems of f&j0;p and p&j0;f where f is a prime transcendental entire function and p is prime polynomial. We shall use methods from local holomorphic dynamics to solve these problems.;In Chapter 3, by using an extended version of Steinmetz's theorem, we prove that certain class of meromorphic functions is pseudo-prime. Hence, we can prove that under certain conditions, R(z) H(z) is pseudo-prime, where R( z) is a non-constant rational function and H( z) is a finite order periodic function. In Chapter 4, we try to find out all possible factorizations of p(z) H(z) when H is an exponential type periodic function and p is a non-constant polynomial. This confirms a conjecture of G. D. Song and C. C. Yang. |
