Removing the Riemann Hypothesis from the pair correlation method for zeros of the Riemann zeta-function

Assuming the Riemann Hypothesis (RH), Montgomery (1973) proved a theorem concerning the pair correlation of nontrivial zeros of the Riemann zeta-function. One consequence of this theorem was that, under RH, at least 2/3 of the zeros are simple. In earlier papers, we have shown an unconditional version of this theorem of Montgomery and how to obtain the same proportion of simple zeros under a much weaker hypothesis than RH. We have furthermore found a connection to finding proportion of zeros on the critical line. This is joint work with Siegfred Alan C. Baluyot, Daniel Alan Goldston, and Caroline L. Turnage-Butterbaugh. As a follow-up to this work, with Daniel Goldston, Junghun Lee and Jordan Schettler, we noticed that Montgomery's Pair Correlation Conjecture can also be formulated without RH. Its implication is that almost all zeros of the Riemann zeta-function are simple and on the critical line.