On a problem of Erdős concerning the zeros of the derivatives of an entire function

Abstract

Let $\{ {S_k}\}$ be any sequence of sets in the complex plane, each of which has no finite limit point. The authors prove, answering affirmatively a question posed by P. Erdös, that there exists a sequence $\{ {n_k}\}$ of positive integers and a transcendental entire function $f(z)$ such that ${f^{({n_k})}}(z) = 0$ if $z \in {S_k}$.