{"paper":{"title":"Zeros of polynomials with four-term recurrence and linear coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Andres Zumba, Khang Tran","submitted_at":"2018-08-21T21:17:46Z","abstract_excerpt":"This paper investigates the zero distribution of a sequence of polynomials $\\left\\{ P_{m}(z)\\right\\} _{m=0}^{\\infty}$ generated by the reciprocal of $1+ct+B(z)t^{2}+A(z)t^{3}$ where $c\\in\\mathbb{R}$ and $A(z)$, $B(z)$ are real linear polynomials. We study necessary and sufficient conditions for the reality of the zeros of $P_{m}(z)$. Under these conditions, we find an explicit interval containing these zeros, whose union forms a dense subset of this interval."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.07133","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"}