English

Schwarz maps of Algebraic Linear Ordinary Differential Equations

Algebraic Geometry 2016-09-22 v2

Abstract

A linear ordinary differential equation is called algebraic if all its solution are algebraic over its field of definition. In this paper we solve the problem of finding closed form solution to algebraic linear ordinary differential equations in terms of standard equations. Furthermore, we obtain a method to compute all algebraic linear ordinary differential equations with rational coefficients by studying their associated Schwarz map through the Picard-Vessiot Theory.

Keywords

Cite

@article{arxiv.1609.00450,
  title  = {Schwarz maps of Algebraic Linear Ordinary Differential Equations},
  author = {Camilo Sanabria Malagón},
  journal= {arXiv preprint arXiv:1609.00450},
  year   = {2016}
}

Comments

29 pages, v2 style corrections and computational examples added

R2 v1 2026-06-22T15:38:16.222Z