where is a real number. Bieberbach proved his conjecture for. The problem of finding an accurate estimate of the coefficients for the class is a. The Bieberbach conjecture is an attractive problem partly because it is easy to Bieberbach, of which the principal result was the second coefficient theorem. The Bieberbach Conjecture. A minor thesis submitted by. Jeffrey S. Rosenthal. January, 1. Introduction. Let S denote the set of all univalent (i.e.

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The th coefficient in the power series of a univalent function should be no greater than. In other words, if.

In more technical terms, “geometric extremality implies metric extremality. The conjecture had been proven for the first six terms the cases3, and 4 were done by Bieberbach, Lowner, and Garabedian and Schiffer, respectivelywas known to be false beberbach only a finite number of indices Haymanand true for a convex or symmetric conjecutre Le Lionnais The general case was proved by Louis de Branges Proceedings of the Symposium on the Occasion of the Proof.


Multivalent Functions, 2nd ed. Cambridge University Press, Monthly 95, Monthly 93, A Guide to Today’s Mathematics. Oxford University Press, pp.

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