• Journal of the Korean Mathematical Society
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• v.51 no.5
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• pp.1029-1044
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• 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.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.601-610
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• 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.