New Proof of the Equation $\sum_{k=1}^\infty \frac{\mu(k)}{k}=0.$
Edmund Landau
TL;DR
This paper provides a new proof of the classical number theory equation involving the Möbius function, originally proven by Landau, through a translation of his doctoral dissertation.
Contribution
It offers a novel proof of the Möbius sum equation, expanding understanding of Landau's original work with a fresh perspective.
Findings
Confirmed the sum of Möbius function over natural numbers equals zero
Provided a new proof method for a classical number theory result
Enhanced historical understanding of Landau's dissertation
Abstract
This is an English translation of Edmund Landau's Doctoral Dissertation.
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Taxonomy
TopicsMathematics and Applications