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We found an explicit form of Faber polynomials for such functions."},"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":"1505.02355","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-05-10T08:55:55Z","cross_cats_sorted":[],"title_canon_sha256":"3ca9d86b0797a148730b950c3600d4d18d13b652fba8f47558e546f0b3c8878b","abstract_canon_sha256":"7613df6bb47418eb305dbea963ead7370d4116de55fa34df8bb0dcb8eb58f1d1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:16:19.023241Z","signature_b64":"KplDhV8Y4xqIEzZiELU9Foq/iyeJqUql2QAb53Eydj8Om7t3mWw8Q9BMo/z71AeUdgPyWB8qKd5dop5uFXn9Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6245b88f6e4dd777599733df15577a27c9f53b8cb9d94b98dd9fb596ea13a64","last_reissued_at":"2026-05-18T02:16:19.022669Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:16:19.022669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Faber Polynomials with common zero","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Viktor Savchuk","submitted_at":"2015-05-10T08:55:55Z","abstract_excerpt":"We describe the two sets of meromorphic univalent functions in the class $\\Sigma$, for which the sequence of Faber polynomials $\\{F_j\\}_{j=1}^\\infty $ have the roots with following properties respectively: $\\sum_{j=1}^{n}|F_j(z_0)|=0<|F_{n+1}(z_0)|, $ $n\\in\\mathbb N, $ and $|F_1(z_0)|> 0=\\sum_{j=2}^{\\infty}|F_j(z_0)|$. 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