{"paper":{"title":"On the generalized Zalcman functional $\\lambda a_n^2-a_{2n-1}$ in the close-to-convex family","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Liulan Li, Saminathan Ponnusamy","submitted_at":"2016-03-23T10:10:05Z","abstract_excerpt":"Let ${\\mathcal S}$ denote the class of all functions $f(z)=z+\\sum_{n=2}^{\\infty}a_{n}z^{n}$ analytic and univalent in the unit disk $\\ID$. For $f\\in {\\mathcal S}$, Zalcman conjectured that $|a_n^2-a_{2n-1}|\\leq (n-1)^2$ for $n\\geq 3$. This conjecture has been verified only certain values of $n$ for $f\\in {\\mathcal S}$ and for all $n\\ge 4$ for the class $\\mathcal C$ of close-to-convex functions (and also for a couple of other classes). In this paper we provide bounds of the generalized Zalcman coefficient functional $|\\lambda a_n^2-a_{2n-1}|$ for functions in $\\mathcal C$ and for all $n\\ge 3$, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07113","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"}