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Erdős problem 1044

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

No current result

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
IsGLB {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

Reported activity

Reported by these sources. Not reviewed here.

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