E. Bailey

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20202022

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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

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…

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 $ζ (1/2 + i t)$