  The complex zeros of the Riemannn zeta-function are identical to the zeros of
the Riemann xi-function, $\xi(s)$. Thus, if the Riemann Hypothesis is true for
the zeta-function, it is true for $\xi(s)$. Since $\xi(s)$ is entire, the zeros
of $\xi'(s)$, its derivative, would then also satisfy a Riemann Hypothesis. We
investigate the pair correlation function of the zeros of $\xi'(s)$ under the
assumption that the Riemann Hypothesis is true. We then deduce consequences
about the size of gaps between these zeros and the proportion of these zeros
that are simple.
