Asher Roberts

activity

20222026

collaborators

3 papers

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

math.PR2023

The Rate of Convergence for Selberg's Central Limit Theorem under the Riemann Hypothesis

Asher Roberts

We assume the Riemann hypothesis to improve upon the rate of convergence of $(lo g lo g lo g T)^{2} / lo g lo g T$ in Selberg's central limit theorem for $lo g ∣ ζ (1/2 + i t) ∣$ given by…

math.PR2022

The Multivariate Rate of Convergence for Selberg's Central Limit Theorem

Asher Roberts

In this paper we quantify the rate of convergence in Selberg's central limit theorem for $lo g ∣ ζ (1/2 + i t) ∣$ based on the method of proof given by Radziwill and Soundararajan. We ach…