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declared disproved (Lean) · formalizederdos:967
False ↔ ∀ (a : ℕ → ℕ), StrictMono a → 1 < a 0 → (Summable fun k => 1 / ↑(a k)) → ∀ (t : ℝ), 1 + ∑' (k : ℕ), Erdos967.summand t (a k) ≠ 0
number theoryanalysisN/A5 sources
declared disproved (Lean) · formalizederdos:990
False ↔ ∃ C, ∀ (f : Polynomial ℂ), f.coeff 0 ≠ 0 → ∀ (α β : ℝ), 0 ≤ α → α ≤ β → β ≤ 2 * Real.pi → |↑(Erdos990.rootArgCount f (Set.Icc α β)) - (β - α) / (2 * Real.pi) * ↑f.natDegree| ≤ C * √(↑f.support.card * Real.log (Erdos990.M f))
analysisN/A6 sources
declared disproved (Lean) · formalizederdos:1043
False ↔ ∀ (f : Polynomial ℂ), f.Monic → f.degree ≥ 1 → ∃ u, ‖u‖ = 1 ∧ MeasureTheory.volume (⇑(ℝ ∙ u).orthogonalProjection '' Erdos1043.levelSet f) ≤ 2
analysisN/A5 sources
declared disproved (Lean) · formalizederdos:1047
False ↔ ∀ (f : Polynomial ℂ) (m : ℕ) (c : ℝ), f.Monic → (f.rootSet ℂ).ncard = m → 0 < c → (Erdos1047.componentsIn (Erdos1047.sublevelSet f c)).ncard = m → ∀ t ∈ Erdos1047.componentsIn (Erdos1047.sublevelSet f c), Convex ℝ t
analysisN/A5 sources
declared disproved (Lean) · formalizederdos:1048
False ↔ ∀ (r : ℝ) (f : Polynomial ℂ), r < 2 → f.Monic → f.degree ≥ 1 → (∀ z ∈ f.roots, ‖z‖ ≤ r) → ∃ z ∈ Erdos1048.openLevelSet f, ENNReal.ofReal (2 - r) < Metric.ediam (connectedComponentIn (Erdos1048.openLevelSet f) z)
analysisN/A5 sources
declared disproved (Lean)erdos:1197
Erdős problem 1197
analysisN/A5 sources

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