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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. We show that this theorem of Montgomery holds unconditionally and in earlier papers, we have shown how to obtain a proportion of simple zeros under a much weaker hypothesis than RH. There are two types of hypotheses we can use, one is a constraint on the location of zeros, and the other is zero density assumption. In the second paper, we have furthermore found a connection to finding proportion of zeros on the critical line. Inspired by a recent preprint of J. Maynard and K. Pratt, we can additionally weaken our assumption by copying the box finitely many times. 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 the 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.