Theorems · Theorem · number theory
DirichletCharacter.LSeriesSummable_twist_vonMangoldt
∀ {N : ℕ} (χ : DirichletCharacter ℂ N) {s : ℂ},
1 < s.re → LSeriesSummable ((fun n => χ ↑n) * fun n => ↑(ArithmeticFunction.vonMangoldt n)) sThe L-series of the twist of the von Mangoldt function Λ by a Dirichlet character χ
converges at s when re s > 1.
- Defined in
- Mathlib.NumberTheory.LSeries.Dirichlet
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 296 from the axioms · uses propext, Classical.choice, Quot.sound
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 · cited by 62,936
- Realstatement · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Complex.ofRealstatement · cited by 1,654
- ZModstatement · cited by 1,024
- Complex.restatement and proof · cited by 882
- ArithmeticFunctionstatement · cited by 290
- DirichletCharacterstatement and proof · cited by 161
- LSeriesSummablestatement · cited by 59
- ArithmeticFunction.vonMangoldtstatement · cited by 40
- DirichletCharacter.LSeriesSummable_mulproof · cited by 2
- ArithmeticFunction.LSeriesSummable_vonMangoldtproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- DirichletCharacter.LSeries_twist_vonMangoldt_eqproof · cited by 2
- ArithmeticFunction.vonMangoldt.LSeries_residueClass_eqproof · cited by 1