Erdős ProblemsComplex analysis
Erdős Problem 516: Limsup Ratio Eq One Of Has Fejer Gaps
Is it true that for all entire functions f = ∑ aₖzⁿₖ such that ∑' 1 / nₖ < ∞, limsup (fun r => ratio r f) atTop = 1?
Mathematical statement
Is it true that for all entire functions f = ∑ aₖzⁿₖ such that ∑' 1 / nₖ < ∞,
limsup (fun r => ratio r f) atTop = 1?
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_516.variants.limsup_ratio_eq_one_of_hasFejerGaps
theorem erdos_516.variants.limsup_ratio_eq_one_of_hasFejerGaps : answer(sorry) ↔ ∀ {f : ℂ → ℂ} {n : ℕ → ℕ} (hn : HasFejerGaps n) {a : ℕ → ℂ} (ha : ∀ n, a n ≠ 0) (hfn : ∀ z, HasSum (fun k => a k * z ^ n k) (f z)), limsup (fun r => ratio r f) atTop = 1 := 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