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A CLASS OF ARITHMETIC FUNCTIONS ON PSL2(Z)

Spiegelhalter, Paul;Zaharescu, Alexandru

  • Received : 2011.12.04
  • Published : 2013.03.31

Abstract

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.

Keywords

$PSL_2(\mathbb{Z})$;Farey fractions;Dirichlet series

References

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Cited by

  1. Analytic continuation and asymptotics of Dirichlet series with partitions vol.433, pp.1, 2016, https://doi.org/10.1016/j.jmaa.2015.07.044

Acknowledgement

Supported by : NSF