There are numerous questions that one can ask about factorization of meromorphic functions. During the past years, many people investigated the factorization theory using different arguments. In this thesis, we first use the gap theory to prove polynomials of the form p(z) = zⁿ + az^m + b are prime, where a, b ∈ C, a ≠ 0, m and n are positive integers, (m, n) = 1 and n m. Then we extend a work by R. Goldstein [8] , F(z) = β(z)e^α(z) + λ(z) is pseudo-prime, where α(z) is a non-constant polynomial of degree m, β(z) and λ(z) are non-constant entire functions of order less than m, to the meromorphic case, i.e.β(z) and λ(z) are non-constant meromorphic functions of order less than m. The proof of this is different from that of R. Goldstein. At last, we have some further discussion about the c...[ Read more ]

There are numerous questions that one can ask about factorization of meromorphic functions. During the past years, many people investigated the factorization theory using different arguments. In this thesis, we first use the gap theory to prove polynomials of the form p(z) = zⁿ + az^m + b are prime, where a, b ∈ C, a ≠ 0, m and n are positive integers, (m, n) = 1 and n > m. Then we extend a work by R. Goldstein [8] , F(z) = β(z)e^α(z) + λ(z) is pseudo-prime, where α(z) is a non-constant polynomial of degree m, β(z) and λ(z) are non-constant entire functions of order less than m, to the meromorphic case, i.e.β(z) and λ(z) are non-constant meromorphic functions of order less than m. The proof of this is different from that of R. Goldstein. At last, we have some further discussion about the composition of a pseudo-prime transcendental function and a polynomial.