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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:

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

Table of Contents

Proofs: 1

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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