# Bieberbach conjecture

- kind: problem
- status: solved (evidence tier V3)
- year: 1916
- authors: Ludwig Bieberbach

**Statement.** The coefficients of a normalized univalent function on the unit disk satisfy $|a_n| \le n$.

Proved for small n one case at a time over seven decades. De Branges's proof was at first met with doubt, partly because he had earlier announced flawed results. A Leningrad seminar verified it, and the key inequality turned out to be a known fact about special functions, found by Askey and Gasper.

*Evidence tier V3 is the import default for a result the curation records as settled in the published record. No formal proof or certificate is attached to this page yet.*

Posed 1916, Ludwig Bieberbach. Closed 1985, Louis de Branges.

## Sources

- [Wikipedia: De Branges's theorem](https://en.wikipedia.org/wiki/De_Branges%27s_theorem)

[Analysis and PDE](/wiki/Space:analysis.md) · [Mathematics](/wiki/Continent:mathematics.md)

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