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So that means that the Riemann Hypothesis is based on the functional equation instead?

\varsigma(s) = \sum^{\infty}_{n=1}n^{-s} If you substitute a trivial zero, let's say -2. Wouldn't it be \varsigma(s) = \sum^{\infty}_{n=1} = 1^2 + 2^2 + 3^2 + 4^2 + . . . How would this series be equals to zero? Thanks