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Recently, Leung disproved this conjecture for $n=2$ and for all $m\\geq3$ and, also, for $n=3$ and for all odd $m\\geq5$. Complementing his work we disprove it for all $m>n\\geq2$ which are simultaneously odd or even and, also, for the case when $m$ is odd, $n$ is even and $n\\leq \\frac{m+1}{2}"},"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":"1612.07242","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-12-21T17:25:00Z","cross_cats_sorted":[],"title_canon_sha256":"1d99358b2434b1205ef47bf7e0f477691d95ccec52232c90150e36835dd3ac33","abstract_canon_sha256":"44bfb1efbd84b06f5061a086fcacc8ce2a79fd45f8384efb6f09160c2b4e6f5f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:20.980059Z","signature_b64":"6ah3k1F64eRnUozaJanuGdNlV0rycpdSRLrqtj49VyujnXhOYvAmqUKCrSYYh206ptyKd+JVSl2TBqw5mHzhDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"37b49a480d4094167aa7b891d757495c0811cf1c1334721257dde2613f7b3627","last_reissued_at":"2026-05-18T00:32:20.979402Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:20.979402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the failure of Bombieri's conjecture for univalent functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Iason Efraimidis","submitted_at":"2016-12-21T17:25:00Z","abstract_excerpt":"A conjecture of Bombieri states that the coefficients of a normalized univalent function $f$ should satisfy $$ \\liminf_{f\\to K} \\frac{n-{\\rm Re\\,}a_n}{m-{\\rm Re\\,}a_m} = \\min_{t\\in{\\mathbb R}} \\, \\frac{n\\sin t -\\sin(nt)}{m\\sin t -\\sin(mt)}, $$ when $f$ approaches the Koebe function $K(z)=\\frac{z}{(1-z)^2}$. 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