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A CLASS OF ARITHMETIC FUNCTIONS ON PSL<sub>2</sub>(Z)
Spiegelhalter, Paul,Zaharescu, Alexandru Korean Mathematical Society 2013 대한수학회보 Vol.50 No.2
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.
A CLASS OF ARITHMETIC FUNCTIONS ON PSL<sub>2</sub>(ℤ), II
Spiegelhalter, Paul,Zaharescu, Alexandru Korean Mathematical Society 2014 대한수학회보 Vol.51 No.2
Atanassov introduced the irrational factor function and the strong restrictive factor function, which he defined as $I(n)=\displaystyle\prod_{p^{\alpha}||n}^{}p^{1/{\alpha}}$ and $R(n)=\displaystyle\prod_{p^{\alpha}||n}^{}p^{{\alpha}-1}$ 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 $PSL_2(\mathbb{Z})$, 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.
A class of arithmetic functions on PSL2(Z)
Paul Spiegelhalter,Alexandru Zaharescu 대한수학회 2013 대한수학회보 Vol.50 No.2
In [3] and [2], Atanassov introduced the two arithmetic func- tions [수식] called the irrational factor and the restrictive factor, respectively. Alkan, Ledoan, Panaitopol, and the authors explore properties of these arith- metic functions in [1], [7], [8] and [9]. In the present paper, we generalize these functions to a larger class of elements of PSL2(Z), and explore some of the properties of these maps.
A CLASS OF ARITHMETIC FUNCTIONS ON PSL2(Z), II
Paul Spiegelhalter,Alexandru Zaharescu 대한수학회 2014 대한수학회보 Vol.51 No.2
Atanassov introduced the irrational factor function and the strong restrictive factor function, which he dened as I(n) = Y pα∥n p1=α and R(n) = Y pα∥n pα-1 in [2] and [3]. Various properties of these functions have been investi- gated by Alkan, Ledoan, Panaitopol, and the authors. In the prequel, we expanded these functions to a class of elements of PSL2(Z), 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.
STRONG AND WEAK ATANASSOV PAIRS
P. SPIEGELHALTER,A. Zaharescu 장전수학회 2011 Proceedings of the Jangjeon mathematical society Vol.14 No.3
We study the irrational factor I(n) and the restrictive factor R(n) introduced by Atanassov and defined by I(n) = [수식],where [수식] is the prime factorization of n. We consider weighted combinations I(n)^aR(n)^b and characterize the pairs (a,b) in order to measure how close n is to being k-power full or k-power free. We also establish an asymptotic formula for weighted averages of the function I(n)^aR(n)^b.