I whant to know if the following proposition holds:
If $f$ is entire, and $p$ is a polynomial such that $$|f(z)| \leq |p(z)|,\forall z \in \mathbb{C}, $$ then there is $c \in \mathbb{C}; f(z)=cp(z)$.
If it is true, how to prove it?
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2https://en.wikipedia.org/wiki/Liouville%27s_theorem_(complex_analysis) – Will Jagy Jul 06 '18 at 19:28
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2That is true for entire functions $p$, not only for polynomials. – Martin R Jul 06 '18 at 19:29