{"paper":{"title":"Explicit zero-free regions for the Riemann zeta-function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andrew Yang, Michael J. Mossinghoff, Timothy S. Trudgian","submitted_at":"2022-12-13T19:16:54Z","abstract_excerpt":"We prove that the Riemann zeta-function $\\zeta(\\sigma + it)$ has no zeros in the region $\\sigma \\geq 1 - 1/(55.241(\\log|t|)^{2/3} (\\log\\log |t|)^{1/3})$ for $|t|\\geq 3$. In addition, we improve the constant in the classical zero-free region, showing that the zeta-function has no zeros in the region $\\sigma \\geq 1 - 1/(5.558691\\log|t|)$ for $|t|\\geq 2$. We also provide new bounds that are useful for intermediate values of $|t|$. Combined, our results improve the largest known zero-free region within the critical strip for $3\\cdot10^{12} \\leq |t|\\leq \\exp(64.1)$ and $|t| \\geq \\exp(1000)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.06867","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2212.06867/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}