Let $f$ be a meromorphic fuction (as the quotient of two entire functions). If $f$ has real values on the unit circle, then how are the zeros and the poles of $f$ located? What can you say about the general form of $f$ ?
meromorphic functions mapping unit circle to the real axis
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complex-analysis
meromorphic-functions
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0Look at the periodic function $f(e^{iz})$ and apply the Schwarz reflection principle? You'd also need to worry about not having a limit point at $\Im(z)=-\infty$. – 2017-02-24
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0Ah! I was looking at old comprehensive exams for an exam coming up and I don't know the Schwarz Reflection Principle (yet). Thanks. – 2017-02-24