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Mar8-12, 02:55 PM
P: 43
Two questions:
1)Quote comes from a textbook:

Each non-constant function analythic function with f(0)=0 is,in a small nbhd of 0, the composition of a conformal map with the nth-power map...The proof is given and I think I am comfortable with it..

My question is a lot simpler (I think): Can we say the same for a function such that f(a)=b?
I am kindly asking someone to explain why one loses no generality if we
assume a=b=f(a)=0.

2) If an analytic function is not zero in a nbhd, what can I say about the derivative there? i.e. what restriction does this impose on f' (f prime)

Around a circle that lies in the nbhd above we should have
# Zeros=Integral (f'/f)=0

Should this not say f'=0 on that circle?
Thank you
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