Erdős problem 509 · problems.science

Let $f(z) ∈ ℂ[z]$ be a monic non-constant polynomial. Can the set $\{z ∈ ℂ : |f(z)| ≤ 1\}$ be covered by a set of closed discs the sum of whose radii is $≤ 2$ ?

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FormalConjectures/ErdosProblems/

509.lean

Retained formal statement4 of 5

Let f(z) ∈ ℂ[z] be a monic non-constant polynomial. Can the set \{z ∈ ℂ : |f(z)| ≤ 1\} be covered by a set of closed discs the sum of whose radii is ≤ 2.59? Solution: True. This is due to Pommerenke.

FormalConjectures/ErdosProblems/509.leanErdos509.erdos_509.variants.Pommerenke_bound3 linesExact file

1True ↔2  ∀ (f : Polynomial ℂ),3    f.Monic → f.natDegree ≠ 0 → ∃ ι, Nonempty (Erdos509.BoundedDiscCover {z | ‖Polynomial.eval z f‖ ≤ 1} 2.59 ι)

SolvedStatement only, no proof

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