On the number variance of zeta zeros and a conjecture of Berry

Assuming the Riemann hypothesis, we prove estimates for variance of real and imaginary part logarithm zeta function in short intervals. We give three different formulations these results. a conjecture Chan how often gaps between zeros can be close to fixed non-zero value, Berry (1988) number non-universal regime. In this range, Gaussian unitary ensemble statistics do not describe distribution zeros. also calculate lower order terms second moment modulus on critical line. Montgomery's pair correlation conjecture, establishes special case Keating Snaith (2000).