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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.

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