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 a_{n} of such a function, normalised as is always possible so that a_{0}is 0 and a_{1} is 1. It then states that |a_{n}| is at most n.
All Wikipedia text
is available under the
terms of the GNU Free Documentation License