Hybrid Statistics of a Random Model of Zeta over Intervals of Varying Length

Christine Chang

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arXiv · 2404.08575

Hybrid Statistics of a Random Model of Zeta over Intervals of Varying Length

Christine Chang

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Abstract

Arguin, Dubach & Hartung recently conjectured that an intermediate regime exists between IID and log-correlated statistics for extreme values of a random model of the Riemann zeta function. For the same model, we prove a matching upper and lower tail for the distribution of its maximum. This tail interpolates between that of the two aforementioned regimes. We apply the result to yield a new sharp estimate on moments over short intervals, generalizing a result by Harper. In particular, we observe a hybrid regime for moments with a distinctive transition to the IID regime for intervals of length larger than $\exp(\sqrt{\log \log T})$.

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Christine Chang. 2024-04-12. Hybrid Statistics of a Random Model of Zeta over Intervals of Varying Length. https://arxiv.org/abs/2404.08575

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