{"paper":{"title":"On logarithmic coefficients of some close-to-convex functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"A. Vasudevarao, Md Firoz Ali","submitted_at":"2016-06-16T12:44:26Z","abstract_excerpt":"The logarithmic coefficients $\\gamma_n$ of an analytic and univalent function $f$ in the unit disk $\\mathbb{D}=\\{z\\in\\mathbb{C}:|z|<1\\}$ with the normalization $f(0)=0=f'(0)-1$ is defined by $\\log \\frac{f(z)}{z}= 2\\sum_{n=1}^{\\infty} \\gamma_n z^n$. Recently, D.K. Thomas [On the logarithmic coefficients of close to convex functions, {\\it Proc. Amer. Math. Soc.} {\\bf 144} (2016), 1681--1687] proved that $|\\gamma_3|\\le \\frac{7}{12}$ for functions in a subclass of close-to-convex functions (with argument $0$) and claimed that the estimate is sharp by providing a form of a extremal function. In the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.05162","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"}