{"paper":{"title":"On the zeros of asymptotically extremal polynomial sequences in the plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Edward B. Saff, Nikos Stylianopoulos","submitted_at":"2014-09-02T14:33:06Z","abstract_excerpt":"Let $E$ be a compact set of positive logarithmic capacity in the complex plane and let $\\{P_n(z)\\}_{1}^{\\infty}$ be a sequence of asymptotically extremal monic polynomials for $E$ in the sense that \\begin{equation*}%\\label{} \\limsup_{n\\to\\infty}\\|P_n\\|_E^{1/n}\\le\\mathrm{cap}(E). \\end{equation*} The purpose of this note is to provide sufficient geometric conditions on $E$ under which the (full) sequence of normalized counting measures of the zeros of $\\{P_n\\}$ converges in the weak-star topology to the equilibrium measure on $E$, as $n\\to\\infty.$ Utilizing an argument of Gardiner and Pommerenk"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0726","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"}