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The Riemann zeta function is the function of one complex variable $s$ defined by the series $\zeta(s) = \sum_{n \geq 1} \frac{1}{n^s}$ when $\operatorname{Re}(s)>1$. It admits a meromorphic continuation to $\mathbb{C}$ with only a simple pole at $1$. This function satisfies a functional equation relating the values at $s$ and $1-s$. This is the most simple example of an $L$-function and a central object of number theory.

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Geometric / physical / probabilistic interpretations of Riemann zeta($n>1$)?

I know I am late to the party here, but a couple of people mentioned different Basel Problem solutions by Pace and Calabi These solutions, along with another one by Zagier and Kontsevich all have gene …