On a certain kind of generalized number-theoretical Möbius function (Q2707911)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a certain kind of generalized number-theoretical Möbius function |
scientific article |
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31 July 2001
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generalized Möbius function
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multiplicative function
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Dirichlet convolution
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group-theoretic properties
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identities
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0.92850345
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0.92822075
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0.9171117
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0.9169986
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0.91604275
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On a certain kind of generalized number-theoretical Möbius function (English)
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For each complex number \(\alpha\), the authors define the generalized Möbius function \(\mu_\alpha\) as \(\mu_\alpha(n)=\prod_{p|n} {\alpha\choose\partial_p(n)} (-1)^{\partial_p(n)}\), where \(n=\prod_{p|n} p^{\partial_p(n)}\) is the canonical factorization of \(n\). In particular, \(\mu_1=\mu\), the classical Möbius function. Basic properties and applications of \(\mu_\alpha\) are given.
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