no. 15-16
Complex Analysis
An extremal problem for a class of entire functions
[Un problème extrêmal pour une classe de fonctions entières]

Présenté par : Paul Malliavin

Eremenko, Alexandre1 ; Yuditskii, Peter2
1 Purdue University, West Lafayette, IN 47907, USA
2 J. Kepler University, Linz A-4040, Austria
Comptes Rendus. Mathématique, Tome 346 (2008) no. 15-16, pp. 825-828.

Soit f une fonction entière d'indicatrice contenue dans l'intervalle [−iσ,iσ], σ>0. Alors la borne supérieure des zéros de f ne dépasse pas cσ, où c≈1,508879 est la solution d'équation,

log(c2+1+c)=1+c−2.
Cette borne est exacte.

Let f be an entire function of the exponential type, such that the indicator diagram is in [−iσ,iσ], σ>0. Then the upper density of f is bounded by cσ, where c≈1.508879 is the unique solution of the equation

log(c2+1+c)=1+c−2.
This bound is optimal.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2008.06.009
Eremenko, Alexandre 1 ; Yuditskii, Peter 2

1 Purdue University, West Lafayette, IN 47907, USA
2 J. Kepler University, Linz A-4040, Austria 
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Eremenko, Alexandre; Yuditskii, Peter. An extremal problem for a class of entire functions. Comptes Rendus. Mathématique, Tome 346 (2008) no. 15-16, pp. 825-828. doi : 10.1016/j.crma.2008.06.009. http://www.numdam.org/articles/10.1016/j.crma.2008.06.009/

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