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Comptes Rendus Mathématique
Volume 346, n° 15-16
pages 825-828 (août 2008)
Doi : 10.1016/j.crma.2008.06.009
Received : 29 May 2008 ;  accepted : 18 June 2008
An extremal problem for a class of entire functions
Un problème extrêmal pour une classe de fonctions entières
 

Alexandre Eremenko a, 1 , Peter Yuditskii b, 2
a Purdue University, West Lafayette, IN 47907, USA 
b J. Kepler University, Linz A-4040, Austria 

Abstract

Let f be an entire function of the exponential type, such that the indicator diagram is in  ,  . Then the upper density of f is bounded by , where   is the unique solution of the equation
log(c2+1+c)=1+c−2. This bound is optimal. To cite this article: A. Eremenko, P. Yuditskii, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

The full text of this article is available in PDF format.
Résumé

Soit f une fonction entière dʼindicatrice contenue dans lʼintervalle  ,  . Alors la borne supérieure des zéros de f ne dépasse pas , où   est la solution dʼéquation,
log(c2+1+c)=1+c−2. Cette borne est exacte. Pour citer cet article : A. Eremenko, P. Yuditskii, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

The full text of this article is available in PDF format.
1  Supported by NSF grant DMS-0555279.
2  Supported by Austrian Fund FWF P20413-N18.


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