{"paper":{"title":"On Convergence Sets of Power Series with Holomorphic Coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Basma Al-Shutnawi, Daowei Ma, Hua Liu","submitted_at":"2017-07-13T10:27:20Z","abstract_excerpt":"We consider convergence sets of formal power series of the form $f(z,t)=\\sum_{n=0}^{\\infty} f_n(z)t^n$, where $f_n(z)$ are holomorphic functions on a domain $\\Omega$ in $\\mathbb{C}$. A subset $E$ of $\\Omega$ is said to be a convergence set in $\\Omega$ if there is a series $f(z,t)$ such that $E$ is exactly the set of points $z$ for which $f(z,t)$ converges as a power series in a single variable $t$ in some neighborhood of the origin. A $\\sigma$-convex set is defined to be the union of a countable collection of polynomially convex compact subsets. We prove that a subset of $\\mathbb{C}$ is a conv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.04054","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"}