(adsbygoogle = window.adsbygoogle || []).push({}); 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!

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# Homework Help: Liouville's theorem - (probably) easy question

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