If $f$ is an entire function with $|f(z)|>|f(\bar{z})|$ for all complex numbers $z$ in the upper half plane. How does this imply that $f$ has no zeros in the upper half plane?
Zeros of an entire function
4
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complex-analysis
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3Where? If you're talking about zeros in the upper half plane then $f(z) = 0$ implies $0>|f(\bar z)|$ which cannot hold. – 2011-09-21
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0@Gortaur: I fixed it; I mean zeros in the upper half plane. – 2011-09-21