{"paper":{"title":"On the zeros of polynomials generated by rational functions with a hyperbolic polynomial type denominator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Khang Tran, Tam\\'as Forg\\'acs","submitted_at":"2016-06-22T22:04:12Z","abstract_excerpt":"This paper investigates the location of the zeros of a sequence of polynomials generated by a rational function with a denominator of the form $G(z,t)=P(t)+zt^{r}$, where the zeros of $P$ are positive and real. We show that every member of a family of such generating functions - parametrized by the degree of $P$ and $r$ - gives rise to a sequence of polynomials $\\{H_{m}(z)\\}_{m=0}^{\\infty}$ that is eventually hyperbolic. Moreover, when $P(0)>0$ the real zeros of the polynomials $H_{m}(z)$ form a dense subset of an interval $I\\subset\\mathbb{R}^{+}$, whose length depends on the particular values"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07125","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"}