Bieberbach conjecture

Bieberbach conjecture

[′bē·bə‚bäk kən‚jek·chər]
(mathematics)
The proposition, proven in 1984, that if a function ƒ(z) is analytic and univalent in the unit disk, and if it has the power series expansion z + a2 z 2+ a3 z 3+ ⋯, then, for all n (n = 2, 3, …), the absolute value of an is equal to or less than n.
References in periodicals archive ?
De Branges [5] solved the Bieberbach conjecture in 1984.
De Branges, A proof of Bieberbach conjecture, Acta Math.
Like many things everybody knows, this is not in fact true: de Branges was fifty-two when he proved the truth of the Bieberbach Conjecture, which had vexed the best minds for seventy years.