Liouville Function - Mathematics & Logic - Pure Mathematics Dictionary Definition Completely multiplicative arithmetic function λ(n)=(-1)^{Ω(n)}, where Ω(n) is the total number of prime factors of n counted with multiplicity; takes values ±1 and extends multiplicativity to prime powers by λ(p^k)=(-1)^k.
Liouville Function - Mathematics & Logic - Pure Mathematics Dictionary Definition Completely multiplicative arithmetic function λ(n)=(-1)^{Ω(n)}, where Ω(n) is the total number of prime factors of n counted with multiplicity; takes values ±1 and extends multiplicativity to prime powers by λ(p^k)=(-1)^k.