OAI/NumberTheory/Ostmann/Arithmetic/MovingSpectatorProduct.lean

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1 declarations, 0 contain sorry, 0 declared as axioms

1. theorem OAI.Ostmann.movingSlotWeight_spectator_product line 12

   Source documentation

   Factor every spectator while retaining the full smooth and arithmetic coefficient. This identity includes zero-support terms.

   theorem movingSlotWeight_spectator_product {σ I : Type*}
       (q : I → ℕ) [∀ i, Fact (q i).Prime]
       (value : σ → ℕ) (childBound pivotBound : ℕ → ℕ)
       (F : MovingSlotState σ → ℤ → ℂ)
       (extra : MovingSlotState σ → ℤ → ℤ → ℤ → ℝ)
       (hextra : ∀ i x s v w, extra x s v w ≠ 0 →
         (historyPivot (movingSlotSystem value childBound pivotBound) x s v w : ZMod (q i)) ≠ 0)
       (g : ∀ i, ZMod (q i) → ℂ) (D : ∀ i, (ZMod (q i))ˣ) (S : Finset I)
       {n : ℕ} (T : MovingSlotData σ n) (t : FrequencyTree ℤ n) (hT : T.Follows t)
       (XL XR : ℕ) :
       recursiveTransferWeight (movingSlotSystem value childBound pivotBound)
           (fun x s => F x s * ∏ i ∈ S, spectatorHistoryLeaf (movingSlotModulus value) (g i) (D i) x s)
   …

   Mentions: OAI.Ostmann.MovingSlotState, OAI.Ostmann.historyPivot, OAI.Ostmann.movingSlotSystem, OAI.Ostmann.MovingSlotData, OAI.Ostmann.FrequencyTree, OAI.Ostmann.recursiveTransferWeight, OAI.Ostmann.spectatorHistoryLeaf, OAI.Ostmann.movingSlotModulus