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Erdős problem 1048

If f∈C[x]f\in \mathbb{C}[x] is a monic polynomial with all roots satisfying ∣z∣≤r\lvert z\rvert \leq r for some r<2r<2, then must {z:∣f(z)∣<1}\{ z: \lvert f(z)\rvert <1\} have a connected component with diameter >2−r>2-r?

No current result

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

Retained declaration

FormalConjectures/ErdosProblems/1048.lean

Formal Conjectures

FormalConjectures/ErdosProblems/1048.leanErdos1048.erdos_10488 linesExact file
False ↔  ∀ (r : ℝ) (f : Polynomial ℂ),    r < 2 →      f.Monic →        f.degree ≥ 1 →          (∀ z ∈ f.roots, ‖z‖ ≤ r) →            ∃ z ∈ Erdos1048.openLevelSet f,              ENNReal.ofReal (2 - r) < Metric.ediam (connectedComponentIn (Erdos1048.openLevelSet f) z)
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:1048
  • PLBY Lean proofsErdosProblems.Erdos1048
  • PLBY Lean proofsErdosProblems.Erdos1048b

Reported activity

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