Theorems · Theorem · number theory
MulChar.sum_one_eq_card_units
∀ {R : Type u_1} [inst : CommMonoid R] [inst_1 : Fintype R] {R' : Type u_2} [inst_2 : CommRing R']
[inst_3 : DecidableEq R], ∑ a, 1 a = ↑(Fintype.card Rˣ)The sum over all values of the trivial multiplicative character on a finite ring is the cardinality of its unit group.
- Defined in
- Mathlib.NumberTheory.MulChar.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
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
- CommRingstatement and proof · cited by 17,173
- Finsetproof · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- Finset.sumstatement · cited by 5,195
- Finset.univstatement and proof · cited by 3,473
- Unitsstatement and proof · cited by 2,804
- Finset.cardproof · cited by 2,327
- Finset.sum_congrproof · cited by 2,323
- CommMonoidstatement and proof · cited by 2,264
- Units.valproof · cited by 1,966
- IsUnitproof · cited by 1,602
Cited by2
Results whose statement or proof uses this declaration.
- jacobiSum_one_nontrivialproof · cited by 1
- gaussSum_one_oneproof · cited by 0