Skip to content

Problems · Vela Mathematics Program

Narrowed toprobability ×Clear all

Problem ledger

15 problemsGraph view
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 provederdos:523
Erdős problem 523
analysisprobabilitypolynomialsN/A
declared openerdos:524
Erdős problem 524
analysisprobabilitypolynomialsN/A3 sources
declared provederdos:525
Erdős problem 525
analysisprobabilitypolynomialspossible
declared solvederdos:526
Erdős problem 526
probabilitygeometryN/A
declared provederdos:527
Erdős problem 527
analysisprobabilityN/A
declared openerdos:529
Erdős problem 529
geometryprobabilityN/A
declared openerdos:1144
Erdős problem 1144
number theoryprobabilityN/A
declared provederdos:1164
Erdős problem 1164
probabilityN/A
declared solvederdos:1165
Erdős problem 1165
probabilityN/A
declared provederdos:1166
Erdős problem 1166
probabilitypossible
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
declared provederdos:1179
Erdős problem 1179
additive combinatoricsprobabilityN/A

Search problems.science

Find a Problem, Result, source, or page