A CLASS OF ARITHMETIC FUNCTIONS ON PSL₂(ℤ), II

Abstract

Atanassov introduced the irrational factor function and the strong restrictive factor function, which he defined as <TEX>$I(n)=\displaystyle\prod_{p^{\alpha}||n}^{}p^{1/{\alpha}}$</TEX> and <TEX>$R(n)=\displaystyle\prod_{p^{\alpha}||n}^{}p^{{\alpha}-1}$</TEX> in [2] and [3]. 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 <TEX>$PSL_2(\mathbb{Z})$</TEX>, 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.

Locations

• Bulletin of the Korean Mathematical Society - View - PDF