Theorems · Theorem · number theory
MulChar.one_apply
∀ {R : Type u_1} [inst : CommMonoid R] {R' : Type u_2} [inst_1 : CommMonoidWithZero R'] {x : R}, IsUnit x → 1 x = 1Evaluation of the trivial character
- Defined in
- Mathlib.NumberTheory.MulChar.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoidCommMonoidWithZero
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.
- DFunLike.coestatement · cited by 62,936
- CommMonoidstatement and proof · cited by 2,264
- IsUnitstatement and proof · cited by 1,602
- CommMonoidWithZerostatement and proof · cited by 913
- IsUnit.unitproof · cited by 252
- MulCharstatement · cited by 186
- MulChar.one_apply_coeproof · cited by 13
Cited by10
Results whose statement or proof uses this declaration.
- DirichletCharacter.modOne_eq_oneproof · cited by 4
- ArithmeticFunction.vonMangoldt.eqOn_LFunctionResidueClassAuxproof · cited by 2
- jacobiSum_one_nontrivialproof · cited by 1
- MulChar.isQuadratic_iff_sq_eq_oneproof · cited by 1
- DirichletCharacter.LFunctionTrivChar_eq_mul_riemannZetaproof · cited by 1
- ArithmeticFunction.LSeries_zeta_eulerProduct_exp_logproof · cited by 1
- riemannZeta_eq_exp_LSeriesproof · cited by 1
- quadraticChar_ne_oneproof · cited by 1
- DirichletCharacter.IsPrimitive.completedLFunction_one_subproof · cited by 0
- gaussSum_one_leftproof · cited by 0