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Definition: Multiplicative Functions

An arithmetic function \(\beta\) with at least one \(m\in\mathbb N\) with \(\beta(m)\neq 0\) is called:

  1. multiplicative, \(\beta(mn)=\beta(m)\beta(n)\) for all relatively prime \(m,n\in\mathbb N\),
  2. completely multiplicative, if \(\beta(mn)=\beta(m)\beta(n)\) for all \(m,n\in\mathbb N\).

| | | | | created: 2014-03-06 17:30:59 | modified: 2019-04-06 07:16:08 | by: bookofproofs | references: [1272]

1.Corollary: Simple Conclusions For Multiplicative Functions

2.Example: Examples of Multiplicative Functions

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Bibliography (further reading)

[1272] Landau, Edmund: “Vorlesungen ├╝ber Zahlentheorie, Aus der Elementaren Zahlentheorie”, S. Hirzel, Leipzig, 1927

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