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Erdős problem 1048

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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?

Erdős Problems records this as disproved (Lean).

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  1. Sourceerdos-problems
  2. StatementRetained
  3. Formal8 retained
  4. Resolutiondisproved (Lean)
  5. WorkNone recorded
  6. DecisionNone here
  7. The questionNot reached
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