Theorems · Definition · number theory
Rat.padicValuation
(p : ℕ) → [Fact (Nat.Prime p)] → Valuation ℚ (WithZero (Multiplicative ℤ))
The p-adic valuation on rationals, sending p to (exp (-1) : ℤᵐ⁰)
- Defined in
- Mathlib.NumberTheory.Padics.PadicNumbers
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 161 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.
Cites7
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
- Nat.Primestatement and proof · cited by 2,059
- Multiplicativestatement · cited by 875
- Valuationstatement · cited by 823
- WithZerostatement · cited by 586
- WithZero.expproof · cited by 112
- padicValRatproof · cited by 49
Cited by26
Results whose statement or proof uses this declaration.
- Int.padicValuationproof · cited by 9
- Rat.HeightOneSpectrum.adicCompletion.padicEquivproof · cited by 5
- Rat.HeightOneSpectrum.adicCompletionIntegers.padicIntEquivproof · cited by 4
- Padic.withValRingEquivstatement and proof · cited by 3
- Padic.withValUniformEquivstatement · cited by 3
- Rat.padicValuation_selfstatement · cited by 2
- Padic.isUniformInducing_cast_withValstatement and proof · cited by 2
- Padic.norm_rat_le_one_iff_padicValuation_le_onestatement · cited by 1
- Padic.withValUniformEquiv_cast_applystatement and proof · cited by 1
- Rat.padicValuation_caststatement · cited by 1
- Rat.padicValuation_le_one_iffstatement and proof · cited by 1
- Padic.isDenseInducing_cast_withValstatement and proof · cited by 1