OAI/NumberTheory/CubicMoment/Estimates/PrimeStoppingCollection.lean
2 declarations, 0 contain sorry, 0 declared as axioms
Exact finite reindexing from choices in the stopping bin to the independent selected and complementary divisor subsets.
- def
OAI.CubicFirstMoment.stoppingDivisorSubsetsline 12 - theorem
OAI.CubicFirstMoment.stopping_subset_sumline 20Source 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