## Werner Georg Nowak

*On the value distribution of a class of arithmetic functions *

Comment.Math.Univ.Carolinae 37,1 (1996) 115-132. **Abstract:**This article deals with the value distribution of multiplicative prime-independent arithmetic functions $(\alpha (n))$ with $\alpha (n)=1$ if $n$ is $N$-free ($N\ge 2$ a fixed integer), $\alpha (n)>1$ else, and $\alpha (2^n)\to \infty $. An asymptotic result is established with an error term probably definitive on the basis of the present knowledge about the zeros of the zeta-function. Applications to the enumerative functions of Abelian groups and of semisimple rings of given finite order are discussed.

**Keywords:** arithmetic functions, value distribution, finite Abelian groups

**AMS Subject Classification:** 11N64, 11N37, 11N45

PDF