Erdős Problem #906

The problem

Is there an entire non-zero function $f:\mathbb{C}\to \mathbb{C}$ such that, for any infinite sequence $n_1<n_2<\cdots$, the set

$$\{ z: f^{(n_k)}(z)=0 \textrm{ for some }k\geq 1\}$$

is everywhere dense?

Statement quoted from erdosproblems.com/906, maintained by Thomas Bloom. Original source: [Er56d][Er82e,p.72]. Current status there: open.

AI contributions

As recorded in Terence Tao's wiki AI contributions to Erdős problems (data as of 30 Jun 2026). 🟢 full, 🟡 partial, ⚪ unverified, 🔴 incorrect.

Caveats

The wiki's classifications are provisional and are not a benchmark. Many Erdős problems have never had a thorough literature review, so a result that looks new may later turn out to be known; some problems were also stated ambiguously or incorrectly. See the problem page for the full discussion.

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