{"paper":{"title":"Note on the resonance method for the Riemann zeta function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andriy Bondarenko, Kristian Seip","submitted_at":"2017-01-18T07:39:08Z","abstract_excerpt":"We improve Montgomery's $\\Omega$-results for $|\\zeta(\\sigma+it)|$ in the strip $1/2<\\sigma<1$ and give in particular lower bounds for the maximum of $|\\zeta(\\sigma+it)|$ on $\\sqrt{T}\\le t \\le T$ that are uniform in $\\sigma$. We give similar lower bounds for the maximum of $|\\sum_{n\\le x} n^{-1/2-it}|$ on intervals of length much larger than $x$. We rely on our recent work on lower bounds for maxima of $|\\zeta(1/2+it)|$ on long intervals, as well as work of Soundararajan, G\\'{a}l, and others. The paper aims at displaying and clarifying the conceptually different combinatorial arguments that sho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04978","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"}