I am interested in doing a video about the geometry of the Riemann zeta function, which is to include diagrams of the critical strip. In all of the diagrams I've seen, zeros are isolated points. I'm not sure that has been proven.
An earlier question referred to the article https://phys.org/news/2017-04-insight-math-million-dollar-problem-riemann.html which states without reference that "One of the most helpful clues for proving the Riemann hypothesis has come from function theory, which reveals that the values of the imaginary part, t, at which the function vanishes are discrete numbers." One of the answers indicated that "discrete" means "isolated."
Can anyone provide a reference for that claim?
Should I draw possible zeros (symmetrically across $\Re(s) = 1/2$) as points, line segments of constant $\Re(s)$, line segments of constant $\Im(s)$, and disks?