- Thread starter
- Moderator
- #1

- Jun 20, 2014

- 1,896

-----

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

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

-----

Remember to read the POTW submission guidelines to find out how to submit your answers!