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Possible Duplicate:
Non zero analytic functions on annulus

Let $f$ be holomorphic on the punctured unit disk $\{z\in\mathbb{C}:0<|z|<1\}$ and suppose $f$ has no zeros. I want to show that there exist an integer $m$ and a function $g$ holomorphic on the punctured unit disk such that $f(z)=z^{m}e^{g(z)}$ for all $z$ in the punctured disk.

I'm not sure how to even start. I thought about considering the Laurent series expansion of $f$ but I didn't get far.

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