{"paper":{"title":"Logarithmic Coefficients and a Coefficient Conjecture for Univalent Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"K.-J. Wirths, M. Obradovi\\'c, S. Ponnusamy","submitted_at":"2017-01-19T13:51:30Z","abstract_excerpt":"Let ${\\mathcal U}(\\lambda)$ denote the family of analytic functions $f(z)$, $f(0)=0=f'(0)-1$, in the unit disk $\\ID$, which satisfy the condition $\\big |\\big (z/f(z)\\big )^{2}f'(z)-1\\big |<\\lambda $ for some $0<\\lambda \\leq 1$. The logarithmic coefficients $\\gamma_n$ of $f$ are defined by the formula $\\log(f(z)/z)=2\\sum_{n=1}^\\infty \\gamma_nz^n$. In a recent paper, the present authors proposed a conjecture that if $f\\in {\\mathcal U}(\\lambda)$ for some $0<\\lambda \\leq 1$, then $|a_n|\\leq \\sum_{k=0}^{n-1}\\lambda ^k$ for $n\\geq 2$ and provided a new proof for the case $n=2$. One of the aims of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.05413","kind":"arxiv","version":2},"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"}