A class of arithmetic functions on \(\mathrm{PSL}_2(\mathbb{Z})\) (Q2857002)
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scientific article; zbMATH DE number 6221357
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A class of arithmetic functions on \(\mathrm{PSL}_2(\mathbb{Z})\) |
scientific article; zbMATH DE number 6221357 |
Statements
31 October 2013
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\(\mathrm{PSL}_2(\mathbb{Z})\)
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Farey fractions
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Dirichlet series
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A class of arithmetic functions on \(\mathrm{PSL}_2(\mathbb{Z})\) (English)
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In [\textit{K. Atanassov}, ``Irrational factor: definition, properties and problems'', Notes Number Theory Discr. Math. 2, No. 3, 42--44 (1996)] and [``Restrictive factor: definition, properties and problems'', ibid. 8, No. 4, 117--119 (2002)], the reviewer introduced the following two arithmetic functions NEWLINE\[NEWLINEI(n) = \prod_{p^{\alpha} || n} p^{1/\alpha} \text{ and } R(n) =\prod_{p^{\alpha} || n} p^{\alpha - 1},NEWLINE\]NEWLINE respectively.NEWLINENEWLINEIn the present paper, generalizations of these functions are introduced, related to a larger class of elements of \(\mathrm{PSL}_2(\mathbb{Z})\). Some interesting properties of the new maps are studied.
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