{"paper":{"title":"Discrepancy bounds for the distribution of the Riemann zeta-function and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.PR"],"primary_cat":"math.NT","authors_text":"Maksym Radziwill, Stephen Lester, Youness Lamzouri","submitted_at":"2014-02-26T20:48:00Z","abstract_excerpt":"We investigate the distribution of the Riemann zeta-function on the line $\\Re(s)=\\sigma$. For $\\tfrac 12 < \\sigma \\le 1$ we obtain an upper bound on the discrepancy between the distribution of $\\zeta(s)$ and that of its random model, improving results of Harman and Matsumoto. Additionally, we examine the distribution of the extreme values of $\\zeta(s)$ inside of the critical strip, strengthening a previous result of the first author.\n  As an application of these results we obtain the first effective error term for the number of solutions to $\\zeta(s) = a$ in a strip $\\tfrac12 < \\sigma_1 < \\sig"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.6682","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"}