Walter Bergweiler, Alexandre Eremenko:

Proof of a conjecture of Polya on the zeros of successive derivatives of real entire functions

We prove Polya'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 n-th derivative tends to infinity with n. 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.

Electronic Print: Front for the Mathematics ArXiv

Mathematics Subject Classification (1991): 30D15; 30E15

Bibliographical note: Acta Math. 197, 125-146 (2006)

Mail an Jens Burmeister

[Thu Feb 19 18:56:37 2009]

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