Solvability of equations by quadratures and Newton's theorem
type: Item
instance of: scholarly article
title: Solvability of equations by quadratures and Newton's theorem
zbMATH Open document ID: 1423.12006
published in: Arnold Mathematical Journal
publication date: 2019-07-25T00:00:00Z
full work available at URL: https://arxiv.org/abs/1808.06328
review text: Let \(F\) be an ordinary differential field and let \(L(y)=0\) be a linear homogeneous differential equation over \(F\). There is an effective dating back to Liouville criterion of solvability in quadratures of the equation. Namely the equation should have a non-trivial solution \(u\) such that \({u}'=au\), where \(a\) is algebraic over \(F\). The author considers that the proof of this fact in the framework of differential algebra is rather involved and offers a simpler proof in the case when \(F\) is a functional differential field.
Mathematics Subject Classification ID: 12H05
Mathematics Subject Classification ID: 34A05
Mathematics Subject Classification ID: 34A09
zbMATH DE Number: 7085224
zbMATH Keywords: linear differential equation
zbMATH Keywords: solvability by quadratures
author: A. G. Khovanskii
reviewed by: Mykola Grygorenko
MaRDI profile type: Publication
OpenAlex ID: W2886927610
arXiv ID: 1808.06328
cites work: Galois Theory, Coverings, and Riemann Surfaces
cites work: Q5787786
cites work: An Analogue of L'Hospital's Rule
cites work: Q4790565
DOI: 10.1007/S40598-018-0091-4
description: scientific article