{"paper":{"title":"Distribution results on polynomials with bounded roots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"J\\\"org Thuswaldner, Peter Kirschenhofer","submitted_at":"2016-09-22T12:51:22Z","abstract_excerpt":"For $d \\in \\mathbb{N}$ the well-known Schur-Cohn region $\\mathcal{E}_d$ consists of all $d$-dimensional vectors $(a_1,\\ldots,a_d)\\in\\mathbb{R}^d$ corresponding to monic polynomials $X^d+a_1X^{d-1}+\\cdots+a_{d-1}X+a_d$ whose roots all lie in the open unit disk. This region has been extensively studied over decades. Recently, Akiyama and Peth\\H{o} considered the subsets $\\mathcal{E}_d^{(s)}$ of the Schur-Cohn region that correspond to polynomials of degree $d$ with exactly $s$ pairs of nonreal roots. They were especially interested in the $d$-dimensional Lebesgue measures $v_d^{(s)}:=\\lambda_d(\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06947","kind":"arxiv","version":2},"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"}