Prime Factorization of Entire Functions

Xinhou Hua; R´emi Vaillancourt

Prime Factorization of Entire Functions

Authors

Xinhou Hua Department of Mathematics and Statistics University of Ottawa, Ottawa, ON, K1N 6N5, Canada.
R´emi Vaillancourt Department of Mathematics and Statistics University of Ottawa, Ottawa, ON, K1N 6N5, Canada.

Keywords:

entire function, unique factorization

Abstract

Let n be a prime number and let f(z) be a transcendental entire function. Then it is proved that both [f(z)+cz]ⁿ and [f(z)+cz]^âˆ’n are uniquely factorizable for any complex number c, except for a countable set in â„‚.