Theorems · Theorem · number theory
ArithmeticFunction.LSeriesSummable_moebius_iff
∀ {s : ℂ}, LSeriesSummable (fun n => ↑(ArithmeticFunction.moebius n)) s ↔ 1 < s.reThe L-series of the Möbius function converges absolutely at s if and only if re s > 1.
- Defined in
- Mathlib.NumberTheory.LSeries.Dirichlet
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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 · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Norm.normproof · cited by 5,413
- Nat.cast_oneproof · cited by 2,501
- absproof · cited by 1,814
- Complex.restatement and proof · cited by 882
- Int.cast_oneproof · cited by 371
- ArithmeticFunctionstatement · cited by 290
- LSeriesSummablestatement and proof · cited by 59
- ArithmeticFunction.moebiusstatement and proof · cited by 45
- Complex.norm_intCastproof · cited by 12
Cited by2
Results whose statement or proof uses this declaration.
- ArithmeticFunction.LSeries_zeta_mul_Lseries_moebiusproof · cited by 2
- DirichletCharacter.LSeries.mul_mu_eq_oneproof · cited by 1