E. Bailey

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math.NT2026

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]:|Î¶(1/2+{\rm i} t)|>(\log T)^k\Big\}\leq C_k \frac{(\log T)^{-k^2}}{\sqrt{\log\lo…

math.NT2024

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

Louis-Pierre Arguin, Emma Bailey

Let $I^´ > 0$ and $I ¨ = \frac{1}{2} + \frac{I ^}{´} lo g T$ . We prove that, for any $I^\pm > 0$ and $V \sim I^\pm lo g lo g T$ as $T \to \infty$ , $\frac{1}{T}\text{meas}\big\{t\in [T,2T]: \log|Î¶(Ï+\rm{…