• 대한수학회지
• /
• 제51권5호
• /
• pp.1029-1044
• /
• 2014

In this paper we consider a generalization of the Mayer-Erd$\ddot{o}$s phenomenon discussed in [12] to linear forms in a larger number of variables.

• 대한수학회보
• /
• 제50권2호
• /
• pp.601-610
• /
• 2013

In [3] and [2], Atanassov introduced the two arithmetic functions $$I(n)=\prod_{p^{\alpha}{\parallel}n}\;p^{1/{\alpha}}\;and\;R(n)=\prod_{p^{\alpha}{\parallel}n}\;p^{{\alpha}-1}$$ called the irrational factor and the restrictive factor, respectively. Alkan, Ledoan, Panaitopol, and the authors explore properties of these arithmetic functions in [1], [7], [8] and [9]. In the present paper, we generalize these functions to a larger class of elements of $PSL_2(\mathbb{Z})$, and explore some of the properties of these maps.