OAI/NumberTheory/TotientAsymptotic/ValueCoverage.lean
1 declarations, 0 contain sorry, 0 declared as axioms
- theorem
OAI.TotientAsymptotic.uncovered_values_negligibleline 14Source documentation
All uncovered values are controlled by the published Ford extraction and the independently proved cofactor and elementary exclusions.
theorem uncovered_values_negligible (_hscale : FordScaleBounds) (hstruct : ExtractedStructureInput) (hbox : FordUnitPrimeBoxInput) (hren : FordRenewalInput) (hmertens : MertensProductInput) : ∃ δ : ℕ → ℝ, Tendsto δ atTop (nhds 0) ∧ ∀ᶠ H : ℕ in atTop, ∀ ε : ℝ, 0<ε → ∀ᶠ x : ℝ in atTop, ∀ t ≤ x, ((uncoveredValues x H t).card : ℝ) ≤ (δ H+ε)*tupleNormalization x := by …Mentions: OAI.TotientAsymptotic.FordScaleBounds, OAI.TotientAsymptotic.ExtractedStructureInput, OAI.TotientAsymptotic.FordUnitPrimeBoxInput, OAI.TotientAsymptotic.FordRenewalInput, OAI.TotientAsymptotic.MertensProductInput, OAI.TotientAsymptotic.uncoveredValues