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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A sharp inequality for the logarithmic coefficients of univalent functions


Author: Oliver Roth
Journal: Proc. Amer. Math. Soc. 135 (2007), 2051-2054
MSC (2000): Primary 30C50; Secondary 30A10
Published electronically: March 2, 2007
MathSciNet review: 2299479
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Abstract | References | Similar Articles | Additional Information

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 $ c_k(f)$ of a normalized univalent function $ f$ in the unit disk.


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Additional Information

Oliver Roth
Affiliation: Mathematisches Institut, Universität Würzburg, D–97074 Würzburg, Germany
Email: roth@mathematik.uni-wuerzburg.de

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08660-1
PII: S 0002-9939(07)08660-1
Keywords: Univalent functions, logarithmic coefficients, de Branges' weight functions
Received by editor(s): September 13, 2005
Received by editor(s) in revised form: January 31, 2006
Published electronically: March 2, 2007
Dedicated: Dedicated to the memory of Professor Nikolaos Danikas
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.