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- Jun 20, 2014

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Consider an analytic map $f : \Bbb D \to \Bbb C$ such that $f(z) = \sum\limits_{n = 0}^\infty a_n z^n$ for all $z\in \Bbb D$. Prove that $f$ is injective, provided

$$\sum_{n = 2}^\infty n\lvert a_n\rvert < \lvert a_1\rvert.$$

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