Theorems · Theorem · number theory
PadicInt.fwdDiff_mahlerSeries
∀ {p : ℕ} [hp : Fact (Nat.Prime p)] {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : Module ℤ_[p] E]
[inst_2 : IsBoundedSMul ℤ_[p] E] [IsUltrametricDist E] [CompleteSpace E] {a : ℕ → E},
Filter.Tendsto a Filter.atTop (nhds 0) → ∀ (n : ℕ), (fwdDiff 1)^[n] (⇑(PadicInt.mahlerSeries a)) 0 = a nThe coefficients of a Mahler series can be recovered from the sum by taking forward differences at
0.
- Defined in
- Mathlib.NumberTheory.Padics.MahlerBasis
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 216 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites36
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- NormedAddCommGroupstatement and proof · cited by 15,752
- nhdsstatement and proof · cited by 5,554
- Finset.sumproof · cited by 5,195
- Filter.Tendstostatement and proof · cited by 3,814
- Factstatement and proof · cited by 2,726
- CompleteSpacestatement and proof · cited by 2,532
- ContinuousMapstatement · cited by 2,491
- Filter.atTopstatement and proof · cited by 2,405
- zero_addproof · cited by 2,366
- Finset.sum_congrproof · cited by 2,323
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.