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Lemma: Upper Bound of Harmonic Series Times Möbius Function

The infinite series built from terms of the harmonic series $\sum_{n=1}^\infty\frac{1}{n}$ multiplied by the Möbius function $\mu(n)$ has the following upper bound:

$$\left|\sum_{n=1}^\infty\frac{\mu(n)}{n}\right|\le 1.$$

| | | | | created: 2019-04-06 21:23:27 | modified: 2019-04-06 22:11:47 | by: bookofproofs | references: [701], [1272]

1.Proof: (related to "Upper Bound of Harmonic Series Times Möbius Function")

Edit or AddNotationAxiomatic Method

This work was contributed under CC BY-SA 3.0 by:

bookofproofs

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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