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2006 Proof of a conjecture of Pólya on the zeros of successive derivatives of real entire functions
Walter Bergweiler, Alexandre Eremenko
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Acta Math. 197(2): 145-166 (2006). DOI: 10.1007/s11511-006-0010-8

Abstract

We prove Pólya’s conjecture of 1943: For a real entire function of order greater than 2 with finitely many non-real zeros, the number of non-real zeros of the nth derivative tends to infinity, as $n\to\infty$. We use the saddle point method and potential theory, combined with the theory of analytic functions with positive imaginary part in the upper half-plane.

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Walter Bergweiler. Alexandre Eremenko. "Proof of a conjecture of Pólya on the zeros of successive derivatives of real entire functions." Acta Math. 197 (2) 145 - 166, 2006. https://doi.org/10.1007/s11511-006-0010-8

Information

Received: 6 December 2005; Published: 2006
First available in Project Euclid: 31 January 2017

zbMATH: 1121.30013
MathSciNet: MR2296054
Digital Object Identifier: 10.1007/s11511-006-0010-8

Rights: 2007 © Institut Mittag-Leffler

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Vol.197 • No. 2 • 2006
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