OAI/NumberTheory/CubicMoment/Estimates/PrimeStoppingCollection.lean

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Exact finite reindexing from choices in the stopping bin to the independent selected and complementary divisor subsets.

  1. def OAI.CubicFirstMoment.stoppingDivisorSubsets line 12
  2. theorem OAI.CubicFirstMoment.stopping_subset_sum line 20

    Source documentation

    This is the finite reindexing behind independent alpha/beta collection; both subsets, and hence all coefficient weights, are exact.

    theorem stopping_subset_sum (s : Finset Eisenstein) (bin : Eisenstein → ℕ)
        (j k : ℕ) (K : Finset Eisenstein → Finset Eisenstein → ℂ) :
        (∑ t ∈ (primeBin s bin j).powersetCard k,
          K (stoppingSelected s bin j t) (stoppingRemainder s bin j t)) =
        ∑ d ∈ stoppingDivisorSubsets s bin j k, K d (s \ d) := by
    …

    Mentions: OAI.CubicFirstMoment.Eisenstein, OAI.CubicFirstMoment.primeBin, OAI.CubicFirstMoment.stoppingSelected, OAI.CubicFirstMoment.stoppingRemainder, OAI.CubicFirstMoment.stoppingDivisorSubsets