Geodesic
On the value distribution of a class of arithmetic functions
Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) no. 1, pp. 117-134.

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This article deals with the value distribution of multiplicative prime-in\-de\-pendent arithmetic functions $(\alpha (n))$ with $\alpha (n)=1$ if $n$ is $N$-free ($N\ge2$ 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.
Classification : 11K65, 11N37, 11N45, 11N64
Keywords: arithmetic functions; value distribution; finite Abelian groups 
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Nowak, Werner Georg. On the value distribution of a class of arithmetic functions. Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) no. 1, pp. 117-134. http://geodesic.mathdoc.fr/item/CMUC_1996__37_1_a6/