Bulletin of the
Korean Mathematical Society BKMS

Atanassov introduced the irrational factor function and the strong restrictive factor function, which he defined as \[ I(n) = \prod_{p^\alpha || n} p^{1/\alpha} \hspace{1cm} \text{ and} \hspace{1cm} R(n) = \prod_{p^\alpha || n} p^{\alpha -1}\] in \cite{MR1429354} and \cite{MR2021015}. Various properties of these functions have been investigated by Alkan, Ledoan, Panaitopol, and the authors. In the prequel, we expanded these functions to a class of elements of $\PSL$, and studied some of the properties of these maps. In the present paper we generalize the previous work by introducing real moments and considering a larger class of maps. This allows us to explore new properties of these arithmetic functions.

Keywords: $\PSL$, Dirichlet series

MSC numbers: Primary 11N37; Secondary 11B99