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Problems · Vela Mathematics Program

Narrowed toformalized ×iterated functions ×Clear all

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declared proved (Lean) · formalizederdos:229
True ↔ ∀ (S : ℕ → Set ℂ), (∀ (n : ℕ), derivedSet (S n) = ∅) → ∃ f, Transcendental (Polynomial ℂ) f ∧ Differentiable ℂ f ∧ ∀ n ≥ 1, ∃ k, ∀ z ∈ S n, iteratedDeriv k f z = 0
analysisiterated functionsN/A5 sources
declared open · formalizederdos:409
∀ (n : ℕ), 0 < n → IsLeast {i | Nat.Prime ((fun x => x.totient + 1)^[i] n)} sorry
number theoryiterated functionsA039651 · A2294872 sources
declared open · formalizederdos:410
True ↔ ∀ n > 1, Filter.Tendsto (fun k => ↑((⇑(ArithmeticFunction.sigma 1))^[k] n) ^ (1 / ↑k)) Filter.atTop Filter.atTop
number theoryiterated functionsA007497 · possible2 sources
declared open · formalizederdos:412
True ↔ ∀ m ≥ 2, ∀ n ≥ 2, ∃ i j, (⇑(ArithmeticFunction.sigma 1))^[i] m = (⇑(ArithmeticFunction.sigma 1))^[j] n
number theoryiterated functionsA007497 · A0515722 sources
declared open · formalizederdos:413
True ↔ {n | Erdos413.IsBarrier (fun m => ↑(ArithmeticFunction.cardDistinctFactors m)) n}.Infinite
number theoryiterated functionsA0052362 sources
declared open · formalizederdos:414
True ↔ ∀ m > 0, ∀ n > 0, ∃ i j, Erdos414.h^[i] m = Erdos414.h^[j] n
number theoryiterated functionsA064491 · possible2 sources
declared open · formalizederdos:906
Is there an entire non-zero function f:C→Cf:\mathbb{C}\to \mathbb{C} such that, for any infinite sequence n1<n2<⋯n_1<n_2<\cdots, the set {z:f(nk)(z)=0 for some k≥1}\{ z: f^{(n_k)}(z)=0 \textrm{ for some }k\geq 1\} is everywhere dense? The literal question is trivial for polynomials, so the claims address the transcendental entire case, in the affirmative.
analysisiterated functionsN/A5 sources

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