A weighted central limit theorem for $\log |\zeta (1/2+it)|$

Alessandro Fazzari

Under the Riemann Hypothesis, we show that as $t$ varies in $T\le t\le 2T$, the distribution of $\log |\zeta (1/2+it)|$ with respect to the measure $|\zeta (1/2+it){|}^{2}dt$ is approximately…