Liouville function
The Liouville function is defined by λ(1)=1 and λ(n)=(-1)k1+k2+⋯+kr, if the prime factorization
of n>1 is n=pk11pk22⋯pkrr (where each pi is positive). This function
is completely multiplicative and the
∑d|nλ(d)={1if n=m2 for some integer m0otherwise, |
where the sum runs over all positive divisors of n.
Title | Liouville function |
---|---|
Canonical name | LiouvilleFunction |
Date of creation | 2013-03-22 11:47:09 |
Last modified on | 2013-03-22 11:47:09 |
Owner | KimJ (5) |
Last modified by | KimJ (5) |
Numerical id | 12 |
Author | KimJ (5) |
Entry type | Definition |
Classification | msc 20G10 |
Classification | msc 11A25 |
Classification | msc 81-00 |