Can someone please explain the concept of a Ramanujan sum in easier language than Wikipedia and its relation to this question. Then, how to calculate the Ramanujan sum:
$$\sum _{n\geq 1}^{\Re } n^{-1/s}$$
To show it equal to:
$$\zeta(1/s)$$
2026-03-25 01:23:57.1774401837
Ramanujan sum. What is it, and how do we calculate it?
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$$\zeta(z):=\sum_{n=1}^\infty \frac{1}{n^z}.$$
Plug in $z=1/s$.