Erdős problem 1047 · problems.science

Let $f\in \mathbb{C}[x]$ be a monic polynomial with $m$ distinct roots, and let $c>0$ be a constant small enough such that $\{ z: \lvert f(z)\rvert\leq c\}$ has $m$ distinct connected components.

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6 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

1047.lean

Retained formal statement2 of 6

Goodman [Go66] proved that one of the three components of $\{ z: \lvert (z^2+1)(z-2)^2\rvert < 5^{3/2}/4\}$ is not convex.

FormalConjectures/ErdosProblems/1047.leanErdos1047.erdos_1047.variants.goodman9 linesExact file

1(Erdos1047.componentsIn2        (Erdos1047.strictSublevelSet ((Polynomial.X ^ 2 + 1) * (Polynomial.X - Polynomial.C 2) ^ 2)3          (5 ^ (3 / 2) / 4))).ncard =4    3 ∧5  ∃6    t ∈7      Erdos1047.componentsIn8        (Erdos1047.strictSublevelSet ((Polynomial.X ^ 2 + 1) * (Polynomial.X - Polynomial.C 2) ^ 2) (5 ^ (3 / 2) / 4)),9    ¬Convex ℝ t

SolvedStatement only, no proof

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