OAI/NumberTheory/JointDickman/Probability/ArithmeticSplitWeights.lean

GitHub source file

5 declarations, 0 contain sorry, 0 declared as axioms

1. theorem OAI.JointDickman.auxiliarySubset_disjoint_small line 11
2. theorem OAI.JointDickman.coefficientPrimeSet_primeProduct line 18
3. theorem OAI.JointDickman.coefficientWeight_primeProduct line 24
4. theorem OAI.JointDickman.regularCoefficientWeight_primeProduct line 35
5. theorem OAI.JointDickman.regular_arithmetic_split_identity line 47

   Source documentation

   On a squarefree site, the arithmetic divisor and quotient weights are exactly B times the fair-retention mass with its two regularity indicators.

   theorem regular_arithmetic_split_identity {B L : ℕ} {τ C : ℝ} {S A : Finset ℕ}
       (hB : 1 < B) (hS : S ⊆ auxiliaryPrimes B) (hA : A ⊆ S) :
       regularCoefficientWeight B L τ C (∏ p ∈ A, p) * regularResidueWeight B L τ C (S \ A) =
         (B : ℝ) * subsetRetentionMass S A *
           (if RegularPrimeSet B L τ C A ∧ RegularPrimeSet B L τ C (S \ A) then 1 else 0) := by
   …

   Mentions: OAI.JointDickman.auxiliaryPrimes, OAI.JointDickman.regularCoefficientWeight, OAI.JointDickman.regularResidueWeight, OAI.JointDickman.subsetRetentionMass, OAI.JointDickman.RegularPrimeSet