{"paper":{"title":"Correlations between real and complex zeros of a random polynomial","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.CV"],"primary_cat":"math.PR","authors_text":"Denis Koleda, Dmitry Zaporozhets, Friedrich G\\\"otze","submitted_at":"2016-10-12T06:37:07Z","abstract_excerpt":"Consider a random polynomial $$ G(z):=\\xi_0+\\xi_1z+\\dots+\\xi_nz^n,\\quad z\\in\\mathbb{C}, $$ where $\\xi_0,\\xi_1,\\dots,\\xi_{n}$ are independent real-valued random variables with probability density functions $f_0,\\dots,f_n$. We give an explicit formula for the mixed $(k,l)$-correlation function $\\rho_{k,l}:\\mathbb{R}^k\\times\\mathbb{C}_+^l \\to\\mathbb{R}_+$ between $k$ real and $l$ complex zeros of $G_n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03610","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"}