{"paper":{"title":"Solvability of Equations by Quadratures and Newton's Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Askold Khovanskii","submitted_at":"2018-08-20T07:25:14Z","abstract_excerpt":"Picard--Vessiot theorem (1910) provides a necessary and sufficient condition for solvability of linear differential equations of order $n$ by quadratures in terms of its Galois group. It is based on the differential Galois theory and is rather involved. J.Liouville in 1839 found an elementary criterium for such solvability for $n=2$. J.F.Ritt simplified Liouville's theorem (1948). In 1973 M. Rosenlicht proved a similar criterium for arbitrary $n$. Rosenlicht work relies on the valuation theory and is not elementary. In these notes we show that the elementary Liouville--Ritt method based on dev"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.06328","kind":"arxiv","version":2},"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"}