Conditional Upper Bounds for Large Deviations and Moments of the Riemann Zeta Function

Louis-Pierre Arguin, Emma Bailey, Asher Roberts

Assuming the Riemann Hypothesis, we show that for $k>0$ $$ \frac{1}{T}\text{meas}\Big\{t\in [T,2T]:|ζ(1/2+{\rm i} t)|>(\log T)^k\Big\}\leq C_k \frac{(\log T)^{-k^2}}{\sqrt{\log\log…