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 $≤ 2e$?
Solution: True. This is due to Cartan.
See *Sur les systèmes de fonctions holomorphes à variétés linéaires
lacunaires et leurs applications*, Henri Cartan,
http://www.numdam.org/article/ASENS_1928_3_45__255_0.pdf
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