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Can a branch point of finite order be turned into a pole?
Posted:
Apr 15, 2009 1:07 AM


Consider a function F : C>C, where C is the field of complex numbers. If F is holomorphic near every point except for 0, and F has a branch point of order N at 0. Then I can show that G(z)=F(z^m) is holomorphic in C\{0}.
Now my question is can we also show that if G has a singularity at 0, it must be either removable or a pole. I can show this via Big Picard's theorem when F is an algebraic function. But can we show this in general? If so what's the trick? Thank you.



