OAI/NumberTheory/TotientAsymptotic/TripleSieveError.lean

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3 declarations, 0 contain sorry, 0 declared as axioms

A polynomial bound for the complete error term of the concrete Selberg sieve.

  1. lemma OAI.TotientAsymptotic.triple_sieve_divisor_weight line 11
  2. lemma OAI.TotientAsymptotic.triplePrimeSieve_error_sum line 26
  3. theorem OAI.TotientAsymptotic.triplePrimeTuples_bound line 69

    Source documentation

    All arithmetic remainders in the three-linear-form sieve are now eliminated.

    theorem triplePrimeTuples_bound (a b X z : ℕ) (y : ℝ) (hy : 1 ≤ y) :
        ((triplePrimeTuples a b X z).card:ℝ) ≤
          X/selbergBoundingSum (triplePrimeSieve a b X z y hy)+2*y^3 :=
    …

    Mentions: OAI.TotientAsymptotic.a, OAI.TotientAsymptotic.triplePrimeTuples, OAI.TotientAsymptotic.triplePrimeSieve