Lower Bounds for the Large Deviations of Selberg's Central Limit Theorem

Louis-Pierre Arguin, Emma Bailey

Let $\delta >0$ and $\sigma =\frac{1}{2}+\frac{\delta }{\log T}$. We prove that, for any $\alpha >0$ and $V\sim \alpha \log \log T$ as $T\to \infty$, $\frac{1}{T}\text{meas}\big\{t\in [T,2T]: \log|ζ(σ+\rm{i} τ)|>…