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Some Properties of the Möbius Function

In this section, we will provide some further elementary properties of the Möbius function and derive the useful Möbius inversion formula for arithmetic functions.

| | | | created: 2019-04-06 08:41:03 | modified: 2019-04-06 22:37:14 | by: bookofproofs | references: [701], [1272]

1.Proposition: Sum of Möbius Function Over Divisors

2.Lemma: Sum of Möbius Function Over Divisors With Division

3.Lemma: Möbius and Floor Functions Combined

4.Lemma: Upper Bound of Harmonic Series Times Möbius Function

5.Theorem: Möbius Inversion Formula

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Bibliography (further reading)

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

[701] Scheid Harald: “Zahlentheorie”, Spektrum Akademischer Verlag, 2003, 3. Auflage

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