L. Arguin

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math.NT2026

The Fyodorov--Hiary--Keating Conjecture on Mesoscopic Intervals

Louis-Pierre Arguin, Jad Hamdan

We derive precise upper bounds for the maximum of the Riemann zeta function on a typical short interval of the critical line. We show that for fixed $I^¸ \in (- 1, 0]$ , large $T$ , and $…

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.NT2026

Lower bounds for the large deviations and moments of the Riemann zeta function on the critical line

Louis-Pierre Arguin, Nathan Creighton

Building on work in \cite{AB24} on the Riemann zeta function at height $T$ off the critical line, we prove an unconditional lower bound on the critical line for real large deviatio…

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{…