On the correlation of shifted values of the Riemann zeta function

Abstract:
In 2007, assuming the Riemann Hypothesis (RH), Soundararajan \cite{Moment}
proved that the 2k-th moments of the Riemann zeta function on the critical
line is bounded by T(log T)^{k^2 + epsilon} for every k positive real
number and every epsilon > 0.

In this talk I will generalize his methods to find upper bounds for
shifted moments. Also I will sketch the proof how we derive their lower
bounds and conjecture asymptotic formulas based on Random matrix model,
which is analogous to Keating and Snaith's work. These upper and lower
bounds suggest that the correlation of |\zeta(1/2 + it + i\alpha_1)| and
|\zeta(1/2 + it + i\alpha_2)| transition at |\alpha_1 - \alpha_2| is
around 1/log T}. In particular these distribution appear independent when
|\alpha_1 - \alpha_2| is much larger than 1/log T.