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

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 ntoinfty. 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. © 2007 Institut Mittag-Leffler.