(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that if [tex]f[/tex] is a meromorphic function [tex]f:\mathbb{C}\rightarrow\mathbb{C}[/tex] with

[tex]|f(z)|^5\leq |z|^6\quad\textrm{for all}\quad z\in\mathbb{C}[/tex]

Then [tex]f(z)=0[/tex] for all [tex]z\in\mathbb{C}[/tex]

2. Relevant equations

Liouville's Theorem

A bounded entire function is constant.

3. The attempt at a solution

I tried applying Liouville's theorem to the quotient [tex]f(z)^5/z^6[/tex] which is bounded by 1 but was unsuccessful in proving that f is constant.

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# Homework Help: Application of Liouville's Theorem (Complex Analysis)

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