On the Zeros of the Derivatives of Real Entire Functions and Wiman's Conjecture

Abstract

Let f be an entire function of finite order, real on the real axis, and possessing only real zeros. A classical problem, proposed by G. P6lya [9], [10] and A. Wiman [1], is to determine, from the Hadamard canonical representation of the function, the number of nonreal zeros of the higher derivatives of f. In this paper we shall prove the following conjecture of Wiman, which has been open since 1915: