{"paper":{"title":"The Fyodorov--Hiary--Keating Conjecture on Mesoscopic Intervals","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.NT","authors_text":"Jad Hamdan, Louis-Pierre Arguin","submitted_at":"2024-05-10T13:44:36Z","abstract_excerpt":"We derive precise upper bounds for the maximum of the Riemann zeta function on a typical short interval of the critical line. We show that for fixed $\\theta\\in(-1,0]$, large $T$, and $y\\geq 2$ satisfying $y=O(\\log\\log T/\\log\\log\\log T)$, the proportion of points $t\\in [T,2T]$ for which \\begin{align*}\n  \\max_{|h|\\leq \\log^\\theta T}\\big|\\zeta(&\\tfrac{1}{2}+it+ih)\\big|>e^{y} \\cdot e^{S\\sqrt{(\\log\\log T)|\\theta|/2}}\\frac{(\\log T)^{(1+\\theta)}}{(\\log\\log T)^{3/4}} \\end{align*}\n  is bounded above by a constant times $y\\exp({-2y-y^2/((1+\\theta)\\log\\log T)})$, where $S=S(t)$ is a quantity whose value "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.06474","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.06474/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}