Riemann Zeta Function nontrivial zeros on a graph

Question

On a graph, the nontrivial zeros of the zeta function are on the critical strip. Because the critical strip is vertical, how can any value on the strip be a zero of the zeta function if it isn't directly on the x-axis? For example, how can one of the zeros, (1/2)+(14.13...)i be a zero if it's above the x-axis? Thanks!

Answer 1

The complex plane has two directions, not only the $x$-axis. If $s=x+iy$ is a zero of the Zeta function, this means $0=\zeta(s)=\zeta(x+iy)$, but $y$ need not be zero (and in fact, is not zero for the nontrivial zeros).