E. Bailey

activity

20192026

most citedOn the moments of the moments of

ζ (1/2 + i t)

10 citations · 24 across the 8 of their papers we have counts for

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

math.NT2024

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

Louis-Pierre Arguin, Emma Bailey

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

math.NT2022

Large Deviation Estimates of Selberg's Central Limit Theorem and Applications

Louis-Pierre Arguin, Emma Bailey

For $V \sim α lo g lo g T$ with $0 < α < 2$ , we prove \[ \frac{1}{T}\text{meas}\{t\in [T,2T]: \log|ζ(1/2+ {\rm i} t)|>V\}\ll \frac{1}{\sqrt{\log\log T}} e^{-V^2/\log\log T}. \] This impro…

math.NT2020★ 10 cited

On the moments of the moments of $ζ (1/2 + i t)$

E. C. Bailey, J. P. Keating

Taking $t$ at random, uniformly from $[0, T]$ , we consider the $k$ th moment, with respect to $t$ , of the random variable corresponding to the $2 β$ th moment of $ζ (1/2 + i x)$ over the i…

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

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

Large Deviation Estimates of Selberg's Central Limit Theorem and Applications

On the moments of the moments of ζ(1/2+it)

On the moments of the moments of $ζ (1/2 + i t)$