erdos_517.fabry

Specification

If `f(z) = ∑ aₖzⁿₖ` is an entire function (with `aₖ ≠ 0` for all `k`) such that `nₖ / k → ∞`, is it true that `f` assumes every value infinitely often?

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Lean 4 Statement

theorem erdos_517.fabry : answer(sorry) ↔ ∀ {f : ℂ → ℂ} {n : ℕ → ℕ} (hn : HasFabryGaps n)
    {a : ℕ → ℂ} (ha : ∀ k, a k ≠ 0) (hf : ∀ z, HasSum (fun k => a k * z ^ n k) (f z)) (z : ℂ),
    {x : ℂ | f x = z}.Infinite

ID: ErdosProblems__517__erdos_517.fabry

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