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 statement3 of 6

Goodman [Go66] constructed an example with simple roots, of degree $4$ .

FormalConjectures/ErdosProblems/1047.leanErdos1047.erdos_1047.variants.goodman_simple_roots7 linesExact file

1∃ f c,2  f.Monic ∧3    f.natDegree = 4 ∧4      (f.rootSet ℂ).ncard = 4 ∧5        0 < c ∧6          (Erdos1047.componentsIn (Erdos1047.sublevelSet f c)).ncard = 4 ∧7            ∃ t ∈ Erdos1047.componentsIn (Erdos1047.sublevelSet f c), ¬Convex ℝ t

SolvedStatement only, no proof

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