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Section: 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.

Table of Contents

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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References

Bibliography

1. Scheid Harald: "Zahlentheorie", Spektrum Akademischer Verlag, 2003, 3rd Edition
2. Landau, Edmund: "Vorlesungen über Zahlentheorie, Aus der Elementaren Zahlentheorie", S. Hirzel, Leipzig, 1927