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Erdős problem 1043

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Erdős Problem 1043: Let f∈C[x]f\in \mathbb{C}[x] be a monic polynomial. Must there exist a straight line ℓ\ell such that the projection of {z:∣f(z)∣≤1}\{ z: \lvert f(z)\rvert\leq 1\} onto ℓ\ell has measure at most 22?

No current result

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

Retained declaration

FormalConjectures/ErdosProblems/1043.lean

Formal Conjectures

FormalConjectures/ErdosProblems/1043.leanErdos1043.erdos_10434 linesExact file
False ↔  ∀ (f : Polynomial ℂ),    f.Monic →      f.degree ≥ 1 → ∃ u, ‖u‖ = 1 ∧ MeasureTheory.volume (⇑(ℝ ∙ u).orthogonalProjection '' Erdos1043.levelSet f) ≤ 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:1043
  • PLBY Lean proofsErdosProblems.Erdos1043

Reported activity

Reported by these sources. Not reviewed here.

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