Theorems · Definition · number theory
ArithmeticFunction.liouville
ArithmeticFunction ℤ
The Liouville function λ(n) defined to be 1 if n has an even number of prime factors
(counting multiplicity) and -1 otherwise.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- ArithmeticFunctionstatement · cited by 290
- ArithmeticFunction.cardFactorsproof · cited by 22
Cited by5
Results whose statement or proof uses this declaration.
- ArithmeticFunction.liouville_applystatement · cited by 3
- ArithmeticFunction.liouville_apply_mulstatement and proof · cited by 1
- ArithmeticFunction.liouville_apply_onestatement · cited by 1
- ArithmeticFunction.liouville_ne_zerostatement · cited by 0
- ArithmeticFunction.isMultiplicative_liouvillestatement · cited by 0