{"paper":{"title":"A note on the maximum of the Riemann zeta function, and log-correlated random variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.NT","authors_text":"Adam J. Harper","submitted_at":"2013-04-02T16:05:35Z","abstract_excerpt":"In recent work, Fyodorov and Keating conjectured the maximum size of $|\\zeta(1/2+it)|$ in a typical interval of length O(1) on the critical line. They did this by modelling the zeta function by the characteristic polynomial of a random matrix; relating the random matrix problem to another problem from statistical mechanics; and applying a heuristic analysis of that problem.\n  In this note we recover a conjecture like that of Fyodorov and Keating, but using a different model for $|\\zeta(1/2+it)|$ in terms of a random Euler product. In this case the probabilistic model reduces to studying the su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0677","kind":"arxiv","version":1},"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"}