{"paper":{"title":"Generalized Zalcman conjecture for convex functions of order $\\alpha$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Jinjing Qiao, Liulan Li, Saminathan Ponnusamy","submitted_at":"2016-03-23T10:16:29Z","abstract_excerpt":"Let $\\mathcal S$ denote the class of all functions of the form $f(z)=z+a_2z^2+a_3z^3+\\cdots$ which are analytic and univalent in the open unit disk $\\ID$ and, for $\\lambda >0$, let $\\Phi_\\lambda (n,f)=\\lambda a_n^2-a_{2n-1}$ denote the generalized Zalcman coefficient functional. Zalcman conjectured that if $f\\in \\mathcal S$, then $|\\Phi_1 (n,f)|\\leq (n-1)^2$ for $n\\ge 3$. The functional of the form $\\Phi_\\lambda (n,f)$ is indeed related to Fekete-Szeg\\H{o} functional of the $n$-th root transform of the corresponding function in $\\mathcal S$. This conjecture has been verified for a certain spec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07116","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"}