{"paper":{"title":"Extreme values of the Riemann zeta function and its argument","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andriy Bondarenko, Kristian Seip","submitted_at":"2017-04-20T14:12:53Z","abstract_excerpt":"We combine our version of the resonance method with certain convolution formulas for $\\zeta(s)$ and $\\log\\, \\zeta(s)$. This leads to a new $\\Omega$ result for $|\\zeta(1/2+it)|$: The maximum of $|\\zeta(1/2+it)|$ on the interval $1 \\le t \\le T$ is at least $\\exp\\left((1+o(1)) \\sqrt{\\log T \\log\\log\\log T/\\log\\log T}\\right)$. We also obtain conditional results for $S(t):=1/\\pi$ times the argument of $\\zeta(1/2+it)$ and $S_1(t):=\\int_0^t S(\\tau)d\\tau$. On the Riemann hypothesis, the maximum of $|S(t)|$ is at least $c \\sqrt{\\log T \\log\\log\\log T/\\log\\log T}$ and the maximum of $S_1(t)$ is at least $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06158","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"}