{"paper":{"title":"Maximum of the Riemann zeta function on a short interval of the critical line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.PR","authors_text":"David Belius, Kannan Soundararajan, Louis-Pierre Arguin, Maksym Radziwi{\\l}{\\l}, Paul Bourgade","submitted_at":"2016-12-27T11:14:49Z","abstract_excerpt":"We prove the leading order of a conjecture by Fyodorov, Hiary and Keating, about the maximum of the Riemann zeta function on random intervals along the critical line. More precisely, as $T \\rightarrow \\infty$ for a set of $t \\in [T, 2T]$ of measure $(1 - o(1)) T$, we have $$ \\max_{|t-u|\\leq 1}\\log\\left|\\zeta\\left(\\tfrac{1}{2}+i u\\right)\\right|=(1 + o(1))\\log\\log T . $$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08575","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}