Theorems · Theorem · number theory
DirichletCharacter.isMultiplicative_toArithmeticFunction
∀ {N : ℕ} {R : Type u_1} [inst : CommMonoidWithZero R] (χ : DirichletCharacter R N),
(toArithmeticFunction fun x => χ ↑x).IsMultiplicativeThe arithmetic function associated to a Dirichlet character is multiplicative.
- Defined in
- Mathlib.NumberTheory.LSeries.Dirichlet
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoidWithZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Nat.cast_oneproof · cited by 2,501
- map_mulproof · cited by 1,137
- ZModstatement · cited by 1,024
- CommMonoidWithZerostatement and proof · cited by 913
- map_oneproof · cited by 861
- Nat.cast_mulproof · cited by 309
- DirichletCharacterstatement and proof · cited by 161
- ArithmeticFunction.IsMultiplicativestatement · cited by 45
- ZeroHom.mk.congr_simpproof · cited by 20
- toArithmeticFunctionstatement · cited by 5
- ArithmeticFunction.IsMultiplicative.iff_ne_zeroproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- DirichletCharacter.isMultiplicative_zetaMulproof · cited by 1