Hybrid Statistics of a Random Model of Zeta over Intervals of Varying Length
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909167892037632 |
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| author | Chang, Christine |
| author_facet | Chang, Christine |
| contents | 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 $\exp(\sqrt{\log \log T})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_08575 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hybrid Statistics of a Random Model of Zeta over Intervals of Varying Length Chang, Christine Probability Number Theory 60G70, 11M06 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 $\exp(\sqrt{\log \log T})$. |
| title | Hybrid Statistics of a Random Model of Zeta over Intervals of Varying Length |
| topic | Probability Number Theory 60G70, 11M06 |
| url | https://arxiv.org/abs/2404.08575 |