{"paper":{"title":"Jointly maximal products in weighted growth spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Janne Gr\\\"ohn, Jos\\'e \\'Angel Pel\\'aez, Jouni R\\\"atty\\\"a","submitted_at":"2012-10-11T18:48:26Z","abstract_excerpt":"It is shown that for any non-decreasing, continuous and unbounded doubling function $\\om$ on $[0,1)$, there exist two analytic infinite products $f_0$ and $f_1$ such that the asymptotic relation $|f_0(z)| + |f_1(z)| \\asymp \\om(|z|)$ is satisfied for all $z$ in the unit disc. It is also shown that both functions $f_j$ for $j=0,1$ satisfy $T(r,f_j)\\asymp\\log\\omega(r)$, as $r\\to1^-$, and hence give examples of analytic functions for which the Nevanlinna characteristic admits the regular slow growth induced by $\\omega$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3318","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"}