{"paper":{"title":"Extreme values for $S_n(\\sigma,t)$ near the critical line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andr\\'es Chirre","submitted_at":"2018-07-31T02:50:47Z","abstract_excerpt":"Let $S(\\sigma,t)=\\frac{1}{\\pi}\\arg\\zeta(\\sigma+it)$ be the argument of the Riemann zeta function at the point $\\sigma+it$ of the critical strip. For $n\\geq 1$ and $t>0$ we define $$ S_{n}(\\sigma,t) = \\int_0^t S_{n-1}(\\sigma,\\tau)\\,d\\tau\\, + \\delta_{n,\\sigma\\,}, $$ where $\\delta_{n,\\sigma}$ is a specific constant depending on $\\sigma$ and $n$. Let $0\\leq \\beta<1$ be a fixed real number. Assuming the Riemann hypothesis, we show lower bounds for the maximum of the function $S_n(\\sigma,t)$ on the interval $T^\\beta\\leq t \\leq T$ and near to the critical line, when $n\\equiv 1\\mod 4$. Similar estimat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11642","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"}