Main Page | See live article | Alphabetical index In complex analysis, the Bieberbach 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 a0 is 0 and a1 is 1. It then states that |an| is at most n. This article is from Wikipedia. All text is available under the terms of the GNU Free Documentation License.