Theorems · Theorem · group theory
AddChar.map_add_eq_mul
∀ {A : Type u_1} {M : Type u_3} [inst : AddMonoid A] [inst_1 : Monoid M] (ψ : AddChar A M) (x y : A),
ψ (x + y) = ψ x * ψ yAn additive character maps sums to products.
- Defined in
- Mathlib.Algebra.Group.AddChar
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Monoidstatement and proof · cited by 3,887
- AddMonoidstatement and proof · cited by 2,864
- AddCharstatement and proof · cited by 286
- AddChar.map_add_eq_mul'proof · cited by 1
Cited by13
Results whose statement or proof uses this declaration.
- VectorFourier.fourierIntegral_convergent_iffproof · cited by 9
- gaussSum_mul_gaussSum_eq_cardproof · cited by 4
- Real.fourier_bilin_convolution_eqproof · cited by 3
- AddChar.sum_eq_iteproof · cited by 3
- AddChar.mulShift_mulproof · cited by 2
- AddChar.sum_eq_zero_of_ne_oneproof · cited by 2
- BoundedContinuousFunction.ext_of_char_eqproof · cited by 1
- BoundedContinuousFunction.char_add_eq_mulproof · cited by 1
- VectorFourier.fourierIntegral_comp_add_rightproof · cited by 1
- gaussSum_mulproof · cited by 1
- Subgroup.relIndex_strictPeriodsproof · cited by 1
- fwdDiff_addChar_eqproof · cited by 1