Theorems · Definition · number theory
Height.totalWeight
(K : Type u_1) → [inst : Field K] → [Height.AdmissibleAbsValues K] → ℕ
The totalWeight of a field with AdmissibleAbsValues is the sum of the multiplicities of
the archimedean places.
- Defined in
- Mathlib.NumberTheory.Height.Basic
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- Multiset.cardproof · cited by 375
- Height.AdmissibleAbsValuesstatement and proof · cited by 110
- Height.AdmissibleAbsValues.archAbsValproof · cited by 28
Cited by18
Results whose statement or proof uses this declaration.
- Height.mulHeight₁_add_lestatement and proof · cited by 2
- Height.mulHeight₁_sum_lestatement · cited by 2
- Height.mulHeight_eval_gestatement and proof · cited by 2
- NumberField.totalWeight_eq_sum_multstatement · cited by 2
- Height.mulHeight_linearMap_apply_lestatement and proof · cited by 2
- NumberField.finite_setOfPred_prod_infinitePlace_iSup_leproof · cited by 2
- Height.logHeight₁_add_lestatement and proof · cited by 1
- Height.mulHeight_eval_ge'proof · cited by 1
- NumberField.totalWeight_eq_finrankstatement · cited by 1
- NumberField.totalWeight_posstatement · cited by 1
- NumberField.exists_nat_le_mulHeight₁proof · cited by 1
- NumberField.finite_setOfPred_mulHeight_nat_leproof · cited by 1