Unit function

The unit function is a completely multiplicative function on the positive integers defined as:

$\epsilon (n)={\begin{cases}1,&{\mbox{if }}n{\mbox{=1}}\\0,&{\mbox{if }}n{>1}\end{cases}}$

It is sometimes called multiplication unit for Dirichlet convolution. It is also written as u(n), not to be confused with $\mu$(n).

Also see:

• Möbius inversion formula

The main article for this category is Multiplicative function.

This category corresponds roughly to MSC 11Nxx Multiplicative number theory; see 11Nxx at MathSciNet and 11Nxx at zbMATH.