{"paper":{"title":"Univalent harmonic mappings with integer or half-integer coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"J. Qiao, S. Ponnusamy","submitted_at":"2012-07-12T05:31:51Z","abstract_excerpt":"Let ${\\mathcal S}$ denote the set of all univalent analytic functions $f(z)=z+\\sum_{n=2}^{\\infty}a_n z^n$ on the unit disk $|z|<1$. In 1946 B. Friedman found that the set $\\mathcal S$ of those functions which have integer coefficients consists of only nine functions. In a recent paper Hiranuma and Sugawa proved that the similar set obtained for the functions with half-integer coefficients consists of twelve functions in addition to the nine. In this paper, the main aim is to discuss the class of all sense-preserving univalent harmonic mappings $f$ on the unit disk with integer or half-integer "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3768","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"}