1. The problem statement, all variables and given/known data If f is an entire function and |f(z)|\leq C|z|^(1/2) for all complex numbers z, where C is a positive constant, show that f is constant. 2. Relevant equations All bounded and entire functions are constant. 3. The attempt at a solution I'm 99% sure this can be easily proven using Liouville's theorem, I'm just having trouble proving that f is bounded above by a constant. What should I do with the |z|^(1/2) term? Thanks for the help!