Erdős Problem #1040

Erdős problem #1040 · erdosproblems.com/1040

For a closed infinite set $F \subseteq \mathbb{C}$, let $\mu(F)$ be the infimum of $|\{z : |f(z)| < 1\}|$ over monic polynomials with zeros in $F$. Is $\mu(F)$ determined only by the transfinite diameter of $F$?

Result

Disproved(see note)

Status

Partial result

AI contribution

AI-discovered

Method

Construction

Field

Potential Theory

Posed by

—

Year posed

1958

Years open

68y

Solved

2026-02

Model

Aletheia (Gemini Deep Think)

Vendor

Google DeepMind

Collaborators

—

Verification

Independently expert-verified

Publication

Announced

Significance

10 / 100*

Disclosed cost

—

Wikipedia

No dedicated article