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Problems · Vela Mathematics Program

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declared open · formalizederdos:520
True ↔ ∃ c > 0, ∀ (Ω : Type) [inst : MeasureTheory.MeasureSpace Ω] [MeasureTheory.IsProbabilityMeasure MeasureTheory.volume] (f : ℕ → Ω → ℝ), Erdos520.IsRademacherMultiplicative f → ∀ᵐ (ω : Ω), Filter.limsup (fun N => ∑ m ∈ Finset.Iic N, f m ω / √(↑N * Real.log (Real.log ↑N))) Filter.atTop = c
number theoryprobabilityN/A2 sources
declared open · formalizederdos:521
False ↔ Erdos521.Claim
analysispolynomialsprobabilityN/A4 sources
declared open · formalizederdos:522
For Pn(z)=∑k=0nεkzkP_n(z) = \sum_{k=0}^n \varepsilon_k z^k with independent uniform signs, does the number RnR_n of roots in ∣z∣≤1|z| \le 1 satisfy Rn/(n/2)→1R_n/(n/2) \to 1 almost surely? The manuscript proves the strong law with Rn=n/2+Oω(n149/150)R_n = n/2 + O_\omega(n^{149/150}).
analysispolynomialsprobabilityN/A4 sources
declared open · formalizederdos:1167
∀ (μ : Cardinal.{u}) (r : ℕ) (ν : Ordinal.ToType 1 → Cardinal.{u}), Combinatorics.cardinalPartitionRel μ r 1 ν ↔ μ ≥ ν Erdos1167.i0
set theoryprobabilityN/A2 sources

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