Erdős problem 1044 · problems.science

Let $f(z)=\prod_{i=1}^n(z-z_i)\in\mathbb{C}[x]$ where $\lvert z_i\rvert\leq 1$ for all $i$ . If $\Lambda(f)$ is the maximum of the lengths of the boundaries of the connected components of $\{ z: \lvert f(z)\rvert<1\}$ then determine the infimum of $\Lambda(f)$ .

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No reviewed Result is current in Vela Mathematics Program. Retained source material is shown below.

Retained declaration

FormalConjectures/ErdosProblems/1044.lean

Formal Conjectures

FormalConjectures/ErdosProblems/1044.leanErdos1044.erdos_10441 lineExact file

1IsGLB {L | ∃ f, Erdos1044.IsAdmissible f ∧ Erdos1044.maxBoundaryLength f = L} 2

SolvedProof has a holelean4external proof

The proof uses `sorry`: part of the argument is written but not proved. Lean accepts the file; it does not accept the theorem.

Proof manifests naming this Problem

Jayyhk Erdős Leanjayyhk:erdos:1044
PLBY Lean proofsErdosProblems.Erdos1044

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