Erdős ProblemsComplex analysis
Erdős Problem 906
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.
Mathematical statement
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.
Statement source: Erdős Problems statement material
Statement terms: Source-specific
Source-specific terms. Therefore does not assert reuse rights beyond attributed display.
Statement artifacts, not proofs
These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.
Pinned Lean formulation 1
erdos_906
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 } := by sorry- Statement source
- Formal Conjectures
- Lean version
- v4.27.0
- Placeholder
- Present; no proof artifact
- Source evidence
- Pinned source index
- Fidelity review
- Community formulation
References