Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.



Re: Can a branch point of finite order be turned into a pole?
Posted:
Apr 15, 2009 4:26 PM


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 postgrads." > in sci.logic.)
I see. So it is false. Thank you.



