Jump to content

Unit function

From Wikipedia, the free 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.[1]

It may be described as the "indicator function of 1" within the set of positive integers. It is also written as (not to be confused with , which generally denotes the Möbius function).

See also

[edit]

References

[edit]
  1. ^ Estrada, Ricardo (1995), "Dirichlet convolution inverses and solution of integral equations", Journal of Integral Equations and Applications, 7 (2): 159–166, doi:10.1216/jiea/1181075867, MR 1355233.