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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
In 1985, Louis de Branges de Bourcia proved the Bieberbach conjecture, i.e., for a univalent function its [n.sup.th] Taylor coefficient is bounded by n (see [3]).
de Branges de Bourcia, A proof of Bieberbach conjecture, Acta Mathematica, (1985), 137-152.
De Branges [5] solved the Bieberbach conjecture in 1984.
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.