Difference between revisions
bieberbach-conjecture
Status and infobox
- status:
—→ solved - tier:
—→ V3 - kind:
—→ problem - year:
—→ 1916 - statement:
—→ The coefficients of a normalized univalent function on the unit disk satisfy $|a_n| \le n$.
Source +21 −0
+---
+title: Bieberbach conjecture
+kind: problem
+status: solved
+tier: V3
+year: 1916
+authors: Ludwig Bieberbach
+statement: The coefficients of a normalized univalent function on the unit disk satisfy $|a_n| \le n$.
+space: analysis
+---
+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)
+
+[[Space:analysis|Analysis and PDE]] · [[Continent:mathematics|Mathematics]]
Revision 44 as rendered
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.