POLYNOMIAL-ARITHMETIC FUNCTIONS

Abstract

Let A(Ω) denote the ring of arithmetic functions f :Ω→ C, where Ω is the set of monic polynomials over a finite field. Some characterizations of completely multiplicative arithmetic functions inA(Ω), using distributive property, are established. A necessary and sufficient condition for the αth power function in A(Ω) to be completely multiplicative is given for all nonzero real numbers α.