Encyclopedia > Bieberbach conjecture

  Article Content

Bieberbach conjecture

In complex analysis, the Bierberbach conjecture states a necessary condition on an analytic function to map the unit disk injectively to itself. The conjecture was proved in 1985 by de Branges, with a proof that was subsequently much shortened by others.

The statement concerns the Taylor coefficients an of such a function, normalised as is always possible so that a0is 0 and a1 is 1. It then states that |an| is at most n.



All Wikipedia text is available under the terms of the GNU Free Documentation License

 
  Search Encyclopedia

Search over one million articles, find something about almost anything!
 
 
  
  Featured Article
Lake Ronkonkoma, New York

... age 18 and over, there are 90.3 males. The median income for a household in the town is $60,209, and the median income for a family is $67,375. Males have a median income ...

 
 
 
This page was created in 39.9 ms