A characterization of a certain class of arithmetical multiplicative functions

  • Biagio Palumbo
Keywords: Multiplicative Arithmetical Functions, Möbius Function

Abstract

The object of this paper is the set of the "arithmetical multiplicative functions", i.e. the functions ℕ --> ℂ for which f(mn)=f(n)f(m), under the condition that m and n have no common factors. This set is a group with respect to the Dirichlet's convolution. We define for such functions the concept of type (briefly, a number that expresses the fact that f(pn) is zero when n is large enough); moreover, we prove that the set of the completely multiplicative functions which do not assume the value zero coincides with the set of the functions whose inverses are of type 1.
Published
1995-12-01
Section
Articoli