{"paper":{"title":"On Polya' Theorem in Several Complex Variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Ozan G\\\"uny\\\"uz, Vyacheslav Zakharyuta","submitted_at":"2016-09-01T12:57:11Z","abstract_excerpt":"Let $K$ be a compact set in $\\mathbb{C}$, $f$ a function analytic in $\\overline{\\mathbb{C}}\\smallsetminus K$ vanishing at $\\infty $. Let $% f\\left( z\\right) =\\sum_{k=0}^{\\infty }a_{k}\\ z^{-k-1}$ be its Taylor expansion at $\\infty $, and $H_{s}\\left( f\\right) =\\det \\left( a_{k+l}\\right) _{k,l=0}^{s}$ the sequence of Hankel determinants. The classical Polya inequality says that \\[ \\limsup\\limits_{s\\rightarrow \\infty }\\left\\vert H_{s}\\left( f\\right) \\right\\vert ^{1/s^{2}}\\leq d\\left( K\\right) , \\]% where $d\\left( K\\right) $ is the transfinite diameter of $K$. Goluzin has shown that for some class"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.00218","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"}