Theorems · Theorem · number theory
ArithmeticFunction.coe_mul_zeta_apply
∀ {R : Type u_1} [inst : Semiring R] {f : ArithmeticFunction R} {x : ℕ},
(f * ↑ArithmeticFunction.zeta) x = ∑ i ∈ x.divisors, f i- Cited by
- 4 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Finset.sumstatement and proof · cited by 5,195
- ArithmeticFunctionstatement and proof · cited by 290
- Nat.divisorsstatement and proof · cited by 137
- ArithmeticFunction.zetastatement · cited by 45
- ArithmeticFunction.natToArithmeticFunctionstatement · cited by 30
- ArithmeticFunction.coe_zeta_mul_applyproof · cited by 4
- ArithmeticFunction.coe_zeta_mul_commproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- ArithmeticFunction.moebius_mul_coe_zetaproof · cited by 4
- ArithmeticFunction.vonMangoldt_mul_zetaproof · cited by 3
- ArithmeticFunction.mul_zeta_applyproof · cited by 0
- ArithmeticFunction.sum_moebius_mul_log_eqproof · cited by 0