Unit function
Encyclopedia
In number theory
, the unit function is a completely multiplicative function
on the positive integers defined as:
It is called the unit function because it is the identity element
for Dirichlet convolution
.
It may be described as the "indicator function of 1" within the set of positive integers. It is also written as u(n) (not to be confused with μ(n)).
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
, the unit function is a completely multiplicative function
Multiplicative function
In number theory, a multiplicative function is an arithmetic function f of the positive integer n with the property that f = 1 and whenevera and b are coprime, then...
on the positive integers defined as:
It is called the unit function because it is the identity element
Identity element
In mathematics, an identity element is a special type of element of a set with respect to a binary operation on that set. It leaves other elements unchanged when combined with them...
for Dirichlet convolution
Dirichlet convolution
In mathematics, the Dirichlet convolution is a binary operation defined for arithmetic functions; it is important in number theory. It was developed by Johann Peter Gustav Lejeune Dirichlet, a German mathematician.-Definition:...
.
It may be described as the "indicator function of 1" within the set of positive integers. It is also written as u(n) (not to be confused with μ(n)).