There are two noteworthy operations on the set of arithmetic functions:
If and are two arithmetic functions, the sum of and , denoted , is given by
and the Dirichlet convolution of and , denoted by , is given by
The set of arithmetic functions, equipped with these two binary operations, forms a commutative ring with unity. The 0 of the ring is the function such that for any positive integer . The 1 of the ring is the function with and for any , and the units of the ring are those arithmetic function such that .
Note that giving a sequence of complex numbers is equivalent to giving an arithmetic function by associating with .
|Date of creation||2013-03-22 13:50:49|
|Last modified on||2013-03-22 13:50:49|
|Last modified by||mathcam (2727)|