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

Table of Contents

Corollaries: 1 Examples: 1

Mentioned in:

Corollaries: 1
Examples: 2
Proofs: 3 4
Propositions: 5

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References

Bibliography

1. Landau, Edmund: "Vorlesungen über Zahlentheorie, Aus der Elementaren Zahlentheorie", S. Hirzel, Leipzig, 1927