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Can somebody provide a visualization of $z=\frac{1}{\zeta(x+iy)}\pm N$ for some large $N$ projected onto the $xz$-plane? I would imagine that if we found any asymptotes converging anywhere other than $x=0.5$ it would disprove the Riemann Hypothesis. This is just a hypothetical idea I had and so I was wondering what complications or flaws there are with this reasoning.

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