Moments of the Riemann zeta function on short intervals of the critical line

Louis-Pierre Arguin, Frédéric Ouimet, Maksym Radziwiłł

We show that as $T\to \infty$, for all $t\in [T,2T]$ outside of a set of measure $\mathrm{o}(T)$, $$ \int_{-(\log T)^θ}^{(\log T)^θ} |ζ(\tfrac 12 + \mathrm{i} t + \mathrm{i} h)|^β…