{"paper":{"title":"An effective universality theorem for the Riemann zeta-function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Maksym Radziwill, Stephen Lester, Youness Lamzouri","submitted_at":"2016-11-30T19:32:42Z","abstract_excerpt":"Let $0<r<1/4$, and $f$ be a non-vanishing continuous function in $|z|\\leq r$, that is analytic in the interior. Voronin's universality theorem asserts that translates of the Riemann zeta function $\\zeta(3/4 + z + it)$ can approximate $f$ uniformly in $|z| < r$ to any given precision $\\varepsilon$, and moreover that the set of such $t \\in [0, T]$ has measure at least $c(\\varepsilon) T$ for some $c(\\varepsilon) > 0$, once $T$ is large enough. This was refined by Bagchi who showed that the measure of such $t \\in [0,T]$ is $(c(\\varepsilon) + o(1)) T$, for all but at most countably many $\\varepsilo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.10325","kind":"arxiv","version":2},"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"}