Pair correlations of zeros of the zeta function and perturbations of operators

The set of zeros of the Riemann zeta function rotated to the real line is regarded as the spectrum of a perturbation of a selfadjoint operator, whose spectrum is a regular sequence, under the assumption that the Riemann hypothesis is true. From this point of view we consider the property of pair correlations of the zeta zeros discovered by H. Montgomery. We will prove that this property cannot be fulfilled for finite-rank perturbations.
The talk is based on the joint work with D. Zaporozhets.