Theorems · Theorem · number theory
PadicInt.mahlerSeries_apply
∀ {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) → ∀ (x : ℤ_[p]), (PadicInt.mahlerSeries a) x = ∑' (n : ℕ), (mahler n) x • a nEvaluation of a Mahler series is just the pointwise sum.
- Defined in
- Mathlib.NumberTheory.Padics.MahlerBasis
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 214 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- 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
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- Nat.Primestatement and proof · cited by 2,059
- tsumstatement and proof · cited by 1,148
Cited by1
Results whose statement or proof uses this declaration.
- PadicInt.mahlerSeries_apply_natproof · cited by 3