I'm a bit stumped on this question. I've been thinking about it, and wanted to perhaps apply the Schwarz Lemma, and or, the argument principle, but I really have no idea how to begin. The question is:
Does there exist a function meromorphic on the complex plane whose set of zeros is precisely the unit circle ?
Any hints or feedback is appreciated : )
Originally I had holomorphic, which was an error. Though I don't know if meromorphic will make a difference.