Is there a surface whose contour projects to the reciprocal of the zeta function?

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Q: Is there a surface whose contour projects to the reciprocal of the zeta function?

I was looking at this picture and was wondering about the projections of contours of surfaces. Can any analytic function be realized as a projection from a higher dimensional space, like a surface to a lower dimensional space?

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Below is the reciprocal of the zeta function for reference:

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