**Definition**: Multiplicative Functions

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

**multiplicative**, \(\beta(mn)=\beta(m)\beta(n)\) for all relatively prime \(m,n\in\mathbb N\),**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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[1272] **Landau, Edmund**: “Vorlesungen über Zahlentheorie, Aus der Elementaren Zahlentheorie”, S. Hirzel, Leipzig, 1927

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