OAI/NumberTheory/TotientAsymptotic/CandidateComparison.lean

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1 declarations, 0 contain sorry, 0 declared as axioms

  1. theorem OAI.TotientAsymptotic.candidate_value_comparison line 14

    Source documentation

    The same negligible error controls every least-preimage interval; it counts all exceptional values and all tuples above them.

    theorem candidate_value_comparison (hscale : FordScaleBounds)
        (hstruct : ExtractedStructureInput)
        (hbox : FordUnitPrimeBoxInput) (hren : FordRenewalInput) (hmertens : MertensProductInput)
        (h26 : FordLemma26Input) (h51 : FordLemma51Input) :
        ∃ δ : ℕ → ℝ, Tendsto δ atTop (nhds 0) ∧
          ∀ᶠ H : ℕ in atTop, ∀ ε : ℝ, 0 < ε → ∀ᶠ x : ℝ in atTop, ∀ k : ℕ,
            |((candidateTuples x H k).card : ℝ)-N k x| ≤ (δ H+ε)*tupleNormalization x := by
    …

    Mentions: OAI.TotientAsymptotic.FordScaleBounds, OAI.TotientAsymptotic.ExtractedStructureInput, OAI.TotientAsymptotic.FordUnitPrimeBoxInput, OAI.TotientAsymptotic.FordRenewalInput, OAI.TotientAsymptotic.MertensProductInput, OAI.TotientAsymptotic.FordLemma26Input, OAI.TotientAsymptotic.FordLemma51Input, OAI.TotientAsymptotic.candidateTuples, OAI.TotientAsymptotic.N