{"paper":{"title":"Coefficients of univalent harmonic mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Anbareeswaran Sairam Kaliraj, Saminathan Ponnusamy, Victor V. Starkov","submitted_at":"2017-03-07T13:32:58Z","abstract_excerpt":"Let $\\mathcal{S}_H^0$ denote the class of all functions $f(z)=h(z)+\\overline{g(z)}=z+\\sum^\\infty_{n=2} a_nz^n +\\overline{\\sum^\\infty_{n=2} b_nz^n}$ that are sense-preserving, harmonic and univalent in the open unit disk $|z|<1$. The coefficient conjecture for $\\mathcal{S}_H^0$ is still \\emph{open} even for $|a_2|$. The aim of this paper is to show that if $f=h+\\overline{g} \\in \\mathcal{S}^0_H$ then $ |a_n| < 5.24 \\times 10^{-6} n^{17}$ and $|b_n| < 2.32 \\times 10^{-7}n^{17}$ for all $n \\geq 3$. Making use of these coefficient estimates, we also obtain radius of univalence of sections of unival"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.02371","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"}