Real entire functions with real zeros and a conjecture of Wiman

Abstract

If f is a real entire function and ff" has only real zeros then f belongs to the Laguerre-Polya class, the closure of the set of real polynomials with real zeros. This result completes a long line of development originating from a conjecture of Wiman in 1914.

arXiv comment17 pages, LaTeX

Cited by in corpus (6)

• Proof of a conjecture of Polya on the zeros of successive derivatives of real entire functions
• Meromorphic functions of one complex variable. A survey
• Non-real zeros of derivatives
• Non-real zeros of linear differential polynomials in real meromorphic functions
• Zeros of derivatives of strictly non-real meromorphic functions
• Non-real zeros of derivatives of meromorphic functions