FormalConjectures.ErdosProblems.«906»

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import FormalConjecturesUtil

Erdős Problem 906

Reference: erdosproblems.com/906


namespace Erdos906

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.

@[category research open, AMS 30]
theorem declaration uses 'sorry'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 } := by⊢ True ↔
  ∃ f,
    Transcendental (Polynomial ℂ) f ∧
      Differentiable ℂ f ∧ ∀ (n : ℕ → ℕ), StrictMono n → Dense {z | ∃ k, iteratedDeriv (n k) f z = 0}
  sorryAll goals completed! 🐙


end Erdos906