{"paper":{"title":"Universal partial sums of Taylor series as functions of the centre of expansion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.FA"],"primary_cat":"math.CV","authors_text":"Christoforos Panagiotis","submitted_at":"2017-10-09T14:20:47Z","abstract_excerpt":"V. Nestoridis conjectured that if $\\Omega$ is a simply connected subset of $\\mathbb{C}$ that does not contain $0$ and $S(\\Omega)$ is the set of all functions $f\\in \\mathcal{H}(\\Omega)$ with the property that the set $\\left\\{T_N(f)(z)\\coloneqq\\sum_{n=0}^N\\dfrac{f^{(n)}(z)}{n!} (-z)^n : N = 0,1,2,\\dots \\right\\}$ is dense in $\\mathcal{H}(\\Omega)$, then $S(\\Omega)$ is a dense $G_\\delta$ set in $\\mathcal{H}(\\Omega)$. We answer the conjecture in the affirmative in the special case where $\\Omega$ is an open disc $D(z_0,r)$ that does not contain $0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03114","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"}