Theorems · Theorem · number theory
NumberField.mixedEmbedding.volume_fundamentalDomain_latticeBasis
∀ (K : Type u_1) [inst : Field K] [inst_1 : NumberField K],
MeasureTheory.volume (ZSpan.fundamentalDomain (NumberField.mixedEmbedding.latticeBasis K)) =
2⁻¹ ^ NumberField.InfinitePlace.nrComplexPlaces K * ↑(NNReal.sqrt ‖NumberField.discr K‖₊)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 304 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldNumberField
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites97
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
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- MeasureTheory.Measurestatement · cited by 10,939
- RingHomproof · cited by 10,189
- ENNRealstatement and proof · cited by 9,879
- Equivproof · cited by 8,337
- Fieldstatement and proof · cited by 7,404
- Complexstatement and proof · cited by 5,565
- Norm.normproof · cited by 5,413
- Algebra.algebraMapproof · cited by 4,706
- NNRealstatement and proof · cited by 4,310
Cited by4
Results whose statement or proof uses this declaration.
- NumberField.hermiteTheorem.minkowskiBound_lt_boundOfDiscBddproof · cited by 2
- NumberField.exists_ne_zero_mem_ideal_of_norm_le_mul_sqrt_discrproof · cited by 2
- NumberField.mixedEmbedding.covolume_idealLatticeproof · cited by 1
- NumberField.mixedEmbedding.covolume_integerLatticeproof · cited by 0