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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1609.00218","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-09-01T12:57:11Z","cross_cats_sorted":[],"title_canon_sha256":"8707df48948b06039fa5e9165cd2246c104190c1b7701fd2ea2ce600cd76e549","abstract_canon_sha256":"60f90fbe4f3582f1665dfe70e1746bd0ac271ecbbb3a43a8cbdf59dfb2750a10"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:26.612424Z","signature_b64":"gFdFIlOmIwGsjyA3WU2y1LjmKRgxC2HBF6rl9xj2bRSPHPL7iEFEqv1TIZEQAHyIERU2sTlwZ6thj9kfB1jkAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e39bf066849668db6d24b97d38b7bad19a75f7b2dfce2dcb585e3542ea1388de","last_reissued_at":"2026-05-18T01:06:26.611960Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:26.611960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $K$. 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