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Topic: Can a branch point of finite order be turned into a pole?
Replies: 2   Last Post: Apr 15, 2009 4:26 PM

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tianran.chen@gmail.com

Posts: 49
Registered: 6/3/05
Re: Can a branch point of finite order be turned into a pole?
Posted: Apr 15, 2009 4:26 PM
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On Apr 15, 6:33 am, David C. Ullrich <dullr...@sprynet.com> wrote:
> On Tue, 14 Apr 2009 22:07:26 -0700 (PDT), Gvnaena Pura
>
> <tianran.c...@gmail.com> wrote:

> >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.

>
> What if F(z) = exp(1/sqrt(z)) ?
>
> David C. Ullrich
>
> "Understanding Godel isn't about following his formal proof.
> That would make a mockery of everything Godel was up to."
> (John Jones, "My talk about Godel to the post-grads."
> in sci.logic.)


I see. So it is false. Thank you.



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