{"paper":{"title":"Conditional estimates on small distances between ordinates of zeros of $\\zeta(s)$ and $\\zeta'(s)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Fan Ge","submitted_at":"2016-04-14T18:10:36Z","abstract_excerpt":"Let $\\beta'+i\\gamma'$ be a zero of $\\zeta'(s)$. In \\cite{GYi} Garaev and Y{\\i}ld{\\i}r{\\i}m proved that there is a zero $\\beta+i\\gamma$ of $\\zeta(s)$ with $\n\\gamma'-\\gamma \\ll \\sqrt{|\\beta'-1/2|} $. Assuming RH, we improve this bound by saving a factor $\\sqrt{\\log\\log\\gamma'}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04243","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"}