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

Title & Authors
A CLASS OF ARITHMETIC FUNCTIONS ON PSL2(ℤ), II
Spiegelhalter, Paul; Zaharescu, Alexandru;

Abstract
Atanassov introduced the irrational factor function and the strong restrictive factor function, which he defined as $\small{I(n)=\displaystyle\prod_{p^{\alpha}||n}^{}p^{1/{\alpha}}}$ and $\small{R(n)=\displaystyle\prod_{p^{\alpha}||n}^{}p^{{\alpha}-1}}$ 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 $\small{PSL_2(\mathbb{Z})}$, 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.
Keywords
$\small{PSL_2(\mathbb{Z})}$;Dirichlet series;
Language
English
Cited by
1.
Analytic continuation and asymptotics of Dirichlet series with partitions, Journal of Mathematical Analysis and Applications, 2016, 433, 1, 74
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