How do I show that an entire function $f(z)$ that satisfies $$ |f(z)|\leq\frac{1}{|Im(z)|} \quad \forall z\in\mathbb C $$ is a constant function?
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3Same idea as here should work: http://math.stackexchange.com/questions/987676/suppose-f-is-entire-and-fz-leq-1-re-z2-for-all-z-show-that-f-i – N. S. Oct 26 '14 at 03:09