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after doing a bit of research on the riemann hypothesis I came along this paragraph, in which I dont understand, especially the first sentence , how would one be able to show that?

It can be shown that [tex] \zeta (s) = 0 [/tex] when s is a negative even integer. The famous Riemann hypothesis concerns the locations of the remaining, ‘nontrivial’ zeros of [tex] \zeta(s)[/tex]. It asserts that they all have real part equal to 1/2.

It would be great if someone could elaborate on what this paragraph actually means? thanxs

also is there anyway I could get a diagram in which would show some kind of pattern to make me understand this? Iv been trying to come up with one on mathematica but I end up getting weird looking things,

steven