Theorems · Definition · number theory
mahler
{p : ℕ} → [hp : Fact (Nat.Prime p)] → ℕ → C(ℤ_[p], ℤ_[p])The k-th Mahler basis function, i.e. the unique continuous function ℤ_[p] → ℤ_[p]
agreeing with n ↦ n.choose k for n ∈ ℕ. See [colmez2010], §1.2.1.
- Defined in
- Mathlib.NumberTheory.Padics.MahlerBasis
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 209 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fact
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Factstatement and proof · cited by 2,726
- ContinuousMapstatement · cited by 2,491
- Nat.Primestatement and proof · cited by 2,059
- PadicIntstatement and proof · cited by 179
- Ring.chooseproof · cited by 43
- PadicInt.continuous_chooseproof · cited by 0
Cited by8
Results whose statement or proof uses this declaration.
- PadicInt.mahlerTermproof · cited by 6
- PadicInt.mahlerTerm_applystatement and proof · cited by 3
- mahler_natCast_eqstatement · cited by 2
- PadicInt.norm_mahlerTermproof · cited by 2
- PadicInt.mahlerSeries_applystatement and proof · cited by 1
- mahler_applystatement · cited by 0
- PadicInt.mahlerTerm_onestatement and proof · cited by 0
- PadicInt.norm_mahler_eqstatement · cited by 0