{"paper":{"title":"Nonlinear Convergence Sets of Divergent Power Series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.CV","authors_text":"Buma L. Fridman, Daowei Ma, Tejinder Neelon","submitted_at":"2011-04-10T15:35:53Z","abstract_excerpt":"A nonlinear generalization of convergence sets of formal power series, in the sense of Abhyankar-Moh, is introduced. Given a family y=\\phi_{s}(t,x)=sb_{1}(x)t+b_{2}(x)t^{2}+... of analytic curves in C\\timesC^{n} passing through the origin, Conv_{\\phi}(f) of a formal power series f(y,t,x)\\inC[[y,t,x]] is defined to be the set of all s\\inC for which the power series f(\\phi_{s}(t,x),t,x) converges as a series in (t,x). We prove that for a subset E\\subsetC there exists a divergent formal power series f(y,t,x)\\inC[[y,t,x]] such that E=Conv_{\\phi}(f) if and only if E is a F_{{\\sigma}} set of zero ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1778","kind":"arxiv","version":5},"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"}