Theorems · Theorem · number theory
ArithmeticFunction.convolution_vonMangoldt_zeta
(LSeries.convolution (fun n => ↑(ArithmeticFunction.vonMangoldt n)) fun n => ↑(ArithmeticFunction.zeta n)) = fun n => Complex.log ↑n
A translation of the relation Λ * ↑ζ = log of (real-valued) arithmetic functions
to an equality of complex sequences.
- Defined in
- Mathlib.NumberTheory.LSeries.Dirichlet
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 193 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- Realstatement and proof · cited by 25,697
- Complexstatement and proof · cited by 5,565
- mul_oneproof · cited by 3,885
- Nat.cast_oneproof · cited by 2,501
- Finset.sum_congrproof · cited by 2,323
- MulZeroClass.mul_zeroproof · cited by 2,091
- Complex.ofRealstatement and proof · cited by 1,654
- CharP.cast_eq_zeroproof · cited by 357
- ArithmeticFunctionstatement and proof · cited by 290
- Complex.logstatement and proof · cited by 187
- Nat.divisorsAntidiagonalproof · cited by 61
Cited by1
Results whose statement or proof uses this declaration.
- ArithmeticFunction.convolution_vonMangoldt_const_oneproof · cited by 1