{"paper":{"title":"Entire functions with prescribed singular values","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Luka Boc Thaler","submitted_at":"2019-08-16T15:34:40Z","abstract_excerpt":"We introduce a new class of entire functions $\\mathcal{E}$ which consists of all $F_0\\in\\mathcal{O}(\\mathbb{C})$ for which there exists a sequence $(F_n)\\in \\mathcal{O}(\\mathbb{C})$ and a sequence $(\\lambda_n)\\in\\mathbb{C}$ satisfying $F_n(z)=\\lambda_{n+1}e^{F_{n+1}(z)}$ for all $n\\geq 0$. This new class is closed under the composition and its is dense in the space of all non-vanishing entire functions. We prove that every closed set $V\\subset \\mathbb{C}$ containing the origin and at least one more point is the set of singular values of some locally univalent function in $\\mathcal{E}$, hence t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06026","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.06026/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}