Theorems · Theorem · number theory
ArithmeticFunction.coe_zeta_smul_apply
∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : MulAction R M]
{f : ArithmeticFunction M} {x : ℕ}, (↑ArithmeticFunction.zeta • f) x = ∑ i ∈ x.divisors, f i- Cited by
- 3 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
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
- Semiringstatement and proof · cited by 13,802
- Finsetproof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- Finset.sumstatement and proof · cited by 5,195
- Nat.cast_oneproof · cited by 2,501
- Finset.sum_congrproof · cited by 2,323
- one_smulproof · cited by 1,374
- MulActionstatement and proof · cited by 1,294
- ArithmeticFunctionstatement and proof · cited by 290
- Nat.divisorsstatement and proof · cited by 137
- Finset.sum_mapproof · cited by 115
Cited by3
Results whose statement or proof uses this declaration.
- ArithmeticFunction.coe_zeta_mul_applyproof · cited by 4
- ArithmeticFunction.sum_eq_iff_sum_smul_moebius_eqproof · cited by 3
- ArithmeticFunction.sum_divisorsAntidiagonal_eq_sum_divisorsproof · cited by 0