Entire Function Problem in Complex Analysis
I am currently working on some review problems in complex analysis and
came upon the following conundrum of a problem.
"If $f(z)$ is an entire function, and satisfies $|f(z^2)|\le|f(z)|^2$,
prove that f(z) is a polynomial."
My intuition tells me to show that f(z) has a pole at infinity by showing
that infinity is not an essential or removable singularity. However, I am
getting stuck after this.
Thanks for the help,
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