- Thread starter
- Moderator
- #1

- Jan 26, 2012

- 995

-----

**Problem**: Prove that if $f$ is holomorphic in the unit disc, bounded and not identically zero, and $z_1,z_2,\ldots,z_n,\ldots$ are its zeros (with $|z_k|<1$), then

\[\sum_n(1-|z_n|)<\infty.\]

-----

**Hint**:

Use Jensen's formula.

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