An unconditional Montgomery theorem for pair correlation of zeros of the Riemann zeta-function

Assuming the Riemann Hypothesis (RH), Montgomery proved a theorem concerning pair correlation of zeros of the Riemann zeta-function. One consequence of this theorem is that, assuming RH, at least 67.9% of the nontrivial zeros are simple. Here we obtain an unconditional form of Montgomery’s theorem and show how to apply it to prove the following result on simple zeros: If all the zeros ρ = β + iγ of the Riemann zeta-function such that T³/⁸ < γ ≤ T satisfy |β − 1/2| < 1/(2 log T), then, as T tends to infinity, at least 61.7% of these zeros are simple. The method of proof neither requires nor provides any information on whether any of these zeros are or are not on the critical line where β = 1/2. We also obtain the same result under the weaker assumption of a strong zero-density hypothesis.