2026/07/23 by Eric Hou
Mathematics · #math.CV
11 Pages
arxiv created 2026/08/01 · arxiv updated 2026/08/04
We construct a transcendental entire function for which every nonempty open subset of the complex plane contains a zero of every sufficiently high derivative. Equivalently, the zero sets along every strictly increasing sequence of derivative orders have dense union. The construction uses a bounded-coefficient random Fock series and a summable estimate for the probability that a derivative is zero-free in a fixed disk. The function satisfies |f(z)|≤√2exp(|z|2) and contradicts Theorem~1 of Boas and Reddy as stated. We also identify the missing uniformity in their proof.