{"paper":{"title":"The estimation of the ratio of two entire functions with the same zeros in the ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"A.A.Shkalikov, V.L.Geynts","submitted_at":"2016-01-16T11:29:17Z","abstract_excerpt":"The paper studies entire functions of finite order of growth for which a representation of the form $\\psi(z) = 1+ O(|z|^{-\\mu}), \\mu >0,$ as $z\\to \\infty$, is valid on a fixed ray of the complex plane. The main result is the following. Assume that the zeros of two functions $\\psi_1, \\psi_2$ of this class coincide in the circle of radius $R$ with the center in zero. Then given arbitrary small $\\delta\\in (0,1)$ and $\\varepsilon >0$ the relation of these functions admits the estimate $|\\psi_1(z)/\\psi_2(z) -1| \\leqslant \\varepsilon R^{-\\mu(1-\\delta)}$ for all $|z|\\leqslant R^{1-\\delta}$, provided "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04696","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"}