In number theory, the '''unit function''' is a completely multiplicative function on the positive integers defined as:

:<math>\varepsilon(n) = \begin{cases} 1, & \mbox{if }n=1 \\ 0, & \mbox{if }n \neq 1 \end{cases} </math>

It is called the unit function because it is the identity element for Dirichlet convolution.<ref>{{citation | last = Estrada | first = Ricardo | doi = 10.1216/jiea/1181075867 | issue = 2 | journal = Journal of Integral Equations and Applications | mr = 1355233 | pages = 159–166 | title = Dirichlet convolution inverses and solution of integral equations | volume = 7 | year = 1995| doi-access = free }}.</ref>

It may be described as the "indicator function of 1" within the set of positive integers. It is also written as <math>u(n)</math> (not to be confused with <math>\mu(n)</math>, which generally denotes the Möbius function).

==See also== * Möbius inversion formula * Heaviside step function * Kronecker delta

==References== {{reflist}}

Category:Multiplicative functions Category:1 (number)

{{numtheory-stub}}