An extremal problem for a class of entire functions

Alexandre Eremenko; Peter Yuditskii

doi:10.1016/j.crma.2008.06.009

An extremal problem for a class of entire functions

Alexandre Eremenko, Peter Yuditskii

Research output: Contribution to journal › Article › peer-review

Abstract

Let f be an entire function of the exponential type, such that the indicator diagram is in [- i σ, i σ], σ > 0. Then the upper density of f is bounded by cσ, where c ≈ 1.508879 is the unique solution of the equationlog (sqrt(c² + 1) + c) = sqrt(1 + c^-2) . This bound is optimal. To cite this article: A. Eremenko, P. Yuditskii, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

Original language	English
Pages (from-to)	825-828
Number of pages	4
Journal	Comptes Rendus Mathematique
Volume	346
Issue number	15-16
DOIs	https://doi.org/10.1016/j.crma.2008.06.009
State	Published - Aug 2008
Externally published	Yes

Bibliographical note

Funding Information:
E-mail addresses: [email protected] (A. Eremenko), [email protected] (P. Yuditskii). 1 Supported by NSF grant DMS-0555279. 2 Supported by Austrian Fund FWF P20413-N18.

Funding

E-mail addresses: [email protected] (A. Eremenko), [email protected] (P. Yuditskii). 1 Supported by NSF grant DMS-0555279. 2 Supported by Austrian Fund FWF P20413-N18.

Funders	Funder number
Austrian Fund FWF	P20413-N18
National Science Foundation	DMS-0555279

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10.1016/j.crma.2008.06.009

Cite this

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title = "An extremal problem for a class of entire functions",

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author = "Alexandre Eremenko and Peter Yuditskii",

note = "Funding Information: E-mail addresses: [email protected] (A. Eremenko), [email protected] (P. Yuditskii). 1 Supported by NSF grant DMS-0555279. 2 Supported by Austrian Fund FWF P20413-N18.",

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An extremal problem for a class of entire functions

Abstract

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