Connection to the Möbius Function
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\sum_{n=1}^{\infty}\frac{\mu(s)}{n^s}\equal\frac{1}{\zeta(s)}
Arithmetical functions are the foundations of Analytic Number Theory. For decades, mathematicians have constructed bridges between these functions and the fundamental problems of mathematics.
An example is the connection between the Möbius Function and the Riemann Zeta. While it may seem innocuous, this equation is crucial for one of the most significant equivalent formulations of the Riemann Hypothesis. We explored this topic in our lesson: The Riemann Hypothesis and the Möbius Function.
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