{"paper":{"title":"An estimate of the second moment of a sampling of the Riemann zeta function on the critical line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Minsuk Yang, Sihun Jo","submitted_at":"2016-06-03T16:39:28Z","abstract_excerpt":"We investigate the second moment of a random sampling $\\zeta(1/2+iX_t)$ of the Riemann zeta function on the critical line. Our main result states that if $X_t$ is an increasing random sampling with gamma distribution, then for all sufficiently large $t$, \\[\\mathbb{E} |\\zeta(1/2+iX_t)|^2 = \\log t + O(\\sqrt{\\log t}\\log\\log t).\\]"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01179","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"}