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

Abstract

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.

26 pages

References in corpus (1)

• Real entire functions with real zeros and a conjecture of Wiman

Cited by in corpus (2)

• On the number of real critical points of logarithmic derivatives and the Hawaii conjecture
• Zeros of derivatives of strictly non-real meromorphic functions