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A sharp inequality for the logarithmic coefficients of univalent functions

Authors:	Oliver Roth

Affiliation:	Mathematisches Institut, Universität Würzburg, D--97074 Würzburg, Germany

Abstract:	We prove the sharp inequality $displaystyle sum limits_{k=1}^{infty} left( frac{k}{k+1} right)^2 vert ... ...{infty} left( frac{k}{k+1} right)^2 frac{1}{k^2}=frac{2 , pi^2-12}{3}$ for the logarithmic coefficients of a normalized univalent function in the unit disk.

Keywords:	Univalent functions logarithmic coefficients de Branges' weight functions

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