{"paper":{"title":"Pseudomoments of the Riemann zeta function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.NT"],"primary_cat":"math.FA","authors_text":"Andriy Bondarenko, Eero Saksman, Jing Zhao, Kristian Seip, Ole Fredrik Brevig","submitted_at":"2017-01-24T12:39:44Z","abstract_excerpt":"The $2$kth pseudomoments of the Riemann zeta function $\\zeta(s)$ are, following Conrey and Gamburd, the $2k$th integral moments of the partial sums of $\\zeta(s)$ on the critical line. For fixed $k>1/2$, these moments are known to grow like $(\\log N)^{k^2}$, where $N$ is the length of the partial sum, but the true order of magnitude remains unknown when $k\\le 1/2$. We deduce new Hardy--Littlewood inequalities and apply one of them to improve on an earlier asymptotic estimate when $k\\to\\infty$. In the case $k<1/2$, we consider pseudomoments of $\\zeta^{\\alpha}(s)$ for $\\alpha>1$ and the question "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06842","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"}