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Hybrid Statistics of a Random Model of Zeta over Intervals of Varying Length
- Publication Year :
- 2024
-
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 $\exp(\sqrt{\log \log T})$.<br />Comment: 22 pages
- Subjects :
- Mathematics - Probability
Mathematics - Number Theory
60G70, 11M06
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2404.08575
- Document Type :
- Working Paper