Theorems · Definition · number theory
padicNorm
ℕ → ℚ → ℚ
If q ≠ 0, the p-adic norm of a rational q is p ^ (-padicValRat p q).
If q = 0, the p-adic norm of q is 0.
- Defined in
- Mathlib.NumberTheory.Padics.PadicNorm
- Cited by
- 83 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- padicValRatproof · cited by 49
Cited by90
Results whose statement or proof uses this declaration.
- Padicproof · cited by 151
- PadicSeqproof · cited by 30
- Padic.valuationproof · cited by 28
- PadicSeq.normproof · cited by 20
- PadicSeq.stationaryPointstatement · cited by 15
- padicNorm.zerostatement · cited by 11
- Padic.norm_eq_zpow_neg_valuationproof · cited by 9
- PadicSeq.stationaryPoint_specstatement · cited by 8
- padicNorm.eq_zpow_of_nonzerostatement · cited by 7
- Padic.eq_padicNormstatement · cited by 6
- PadicInt.ofIntSeqstatement and proof · cited by 6
- Rat.AbsoluteValue.padicproof · cited by 6