Theorems · Theorem · number theory
ArithmeticFunction.IsMultiplicative.map_mul_of_coprime
∀ {R : Type u_1} [inst : MonoidWithZero R] {f : ArithmeticFunction R},
f.IsMultiplicative → ∀ {m n : ℕ}, m.gcd n = 1 → f (m * n) = f m * f n- Cited by
- 9 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext
- Assumes
- MonoidWithZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- MonoidWithZerostatement and proof · cited by 456
- ArithmeticFunctionstatement and proof · cited by 290
- ArithmeticFunction.IsMultiplicativestatement and proof · cited by 45
Cited by9
Results whose statement or proof uses this declaration.
- ArithmeticFunction.IsMultiplicative.mulproof · cited by 5
- ArithmeticFunction.moebius_mul_coe_zetaproof · cited by 4
- ArithmeticFunction.IsMultiplicative.pmulproof · cited by 3
- ArithmeticFunction.IsMultiplicative.map_prodproof · cited by 1
- BoundingSieve.inv_selbergTerms_eq_sum_divisors_moebius_nuproof · cited by 1
- ArithmeticFunction.IsMultiplicative.eq_zero_of_squarefree_of_dvd_eq_zeroproof · cited by 0
- Nat.Coprime.sum_divisors_mulproof · cited by 0
- ArithmeticFunction.IsMultiplicative.pdivproof · cited by 0
- Nat.Coprime.card_divisors_mulproof · cited by 0