erdos_906

Specification

Does there exists an entire non-zero transcendental function `f : ℂ → ℂ` such that for any sequence `n₀ < n₁ < ...`, `{ z | ∃ k, iteratedDeriv (n k) f z = 0 }` is dense.

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Lean 4 Statement

theorem erdos_906 : answer(sorry) ↔ ∃ f : ℂ → ℂ, Transcendental (Polynomial ℂ) f ∧
    Differentiable ℂ f ∧ ∀ n : ℕ → ℕ, StrictMono n →
    Dense { z | ∃ k, iteratedDeriv (n k) f z = 0 }

ID: ErdosProblems__906__erdos_906

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