{"paper":{"title":"Pair correlation of roots of rational functions with rational generating functions and quadratic denominators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Alexandru Zaharescu, Khang Tran","submitted_at":"2016-01-18T01:29:07Z","abstract_excerpt":"For any rational functions with complex coefficients $A(z), B(z)$ and $C(z)$, where $A(z)$, $C(z)$ are not identically zero, we consider the sequence of rational functions $H_{m}(z)$ with generating function $\\sum H_{m}(z)t^{m}=1/(A(z)t^{2}+B(z)t+C(z))$. We provide an explicit formula for the limiting pair correlation function of the roots of $\\prod_{m=0}^{n}H_{m}(z)$, as $n\\rightarrow\\infty$, counting multiplicities, on certain closed subarcs $J$ of a curve $\\mathcal{C}$ where the roots lie. We give an example where the limiting pair correlation function does not exist if $J$ contains the end"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04381","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"}