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.
Citation
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
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