OAI/NumberTheory/TotientAsymptotic/ShiftedSieveError.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.odd_sieve_divisor_weight line 11
  2. lemma OAI.TotientAsymptotic.shiftedPrimeSieve_error_sum line 27
  3. theorem OAI.TotientAsymptotic.shiftedPrimePairs_bound line 70

    Source documentation

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

    theorem shiftedPrimePairs_bound (b X z : ℕ) (y : ℝ) (hy : 1 ≤ y) :
        ((shiftedPrimePairs b X z).card:ℝ) ≤
          X/selbergBoundingSum (shiftedPrimeSieve b X z y hy)+2*y^3 :=
    …

    Mentions: OAI.TotientAsymptotic.shiftedPrimePairs, OAI.TotientAsymptotic.shiftedPrimeSieve