- #1

binbagsss

- 1,281

- 11

## Homework Statement

[/B]

Hi

Theorem attached and proof.

I am stuck on

1) Where we get ##|g(z)|\geq |a_m|/2 ## comes from

so ##a_{m}## is the first non-zero Fourier coeffient. So I think this term is ##< |a_m|r^{m}##, from ##r## the radius of the open set, but I don't know how to take care of the rest of the higher tems through ##a_{m}## , is this some theorem or?

2) The conclusion thus ##f(z)## has only one zero at ##z=z_0##

I think I'm being stupid but what is this being made from?

We know ##g(z_0) = a_{m} \neq 0 ## and ##a_{0}=0##, but I don't understand.

Thanks

## Homework Equations

above

## The Attempt at a Solution

above