{"paper":{"title":"High pseudomoments of the Riemann zeta function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ole Fredrik Brevig, Winston Heap","submitted_at":"2018-05-10T08:35:51Z","abstract_excerpt":"The pseudomoments of the Riemann zeta function, denoted $\\mathcal{M}_k(N)$, are defined as the $2k$th integral moments of the $N$th partial sum of $\\zeta(s)$ on the critical line. We improve the upper and lower bounds for the constants in the estimate $\\mathcal{M}_k(N) \\asymp_k (\\log{N})^{k^2}$ as $N\\to\\infty$ for fixed $k\\geq1$, thereby determining the two first terms of the asymptotic expansion. We also investigate uniform ranges of $k$ where this improved estimate holds and when $\\mathcal{M}_k(N)$ may be lower bounded by the $2k$th power of the $L^\\infty$ norm of the $N$th partial sum of $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.03881","kind":"arxiv","version":2},"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"}