OAI/NumberTheory/TotientAsymptotic/ValueCoverage.lean

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1 declarations, 0 contain sorry, 0 declared as axioms

  1. theorem OAI.TotientAsymptotic.uncovered_values_negligible line 14

    Source 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