{"paper":{"title":"Joint universality and generalized strong recurrence with rational parameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"{\\L}ukasz Pa\\'nkowski","submitted_at":"2015-03-24T07:10:22Z","abstract_excerpt":"We prove that, for every rational $d\\ne 0,\\pm 1$ and every compact set $K\\subset\\{s\\in\\mathbb{C}:1/2<\\Re(s)<1\\}$ with connected complement, any analytic non-vanishing functions $f_1,f_2$ on $K$ can be approximated, uniformly on $K$, by the shifts $\\zeta(s+i\\tau)$ and $\\zeta(s+id\\tau)$, respectively. As a consequence we deduce that the set of $\\tau$ satisfying $|\\zeta(s+i\\tau)-\\zeta(s+id\\tau)|<\\varepsilon$ uniformly on $K$ has a positive lower density for every $d\\ne 0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06931","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"}