Consider an interval of length $(\log T)^{\theta}$ for some fixed $\theta > −1$, around a point $1/2 + i y$ on the critical line where $y\in[T,2T]$ and $T$ is large. How do the correlations between the points $t$ for which $\log|\zeta|(1/2 + i (t + y))$ is above a given threshold compare with the correlations between the nontrivial zeros on the same interval ?
Basically, my question boils down to this: Is there a way to reformulate the Montgomery pair correlation conjecture in terms of high points of $\log|\zeta|$ instead of the zeros of zeta ?
