Submission date: 7 September 2012.

Abstract:

We prove that if y” = f(y,y',t) is a generic Painlevé equation from among the classes II to V then any collection of distinct solutions and their derivatives are algebraically independent over C(t). (Already proved by Nishioka for the single Painlevé I equation). For generic Painlevé VI we prove a slightly weaker statement.

Mathematics Subject Classification: 14H05, 14H70, 34M55, 03C60

Keywords and phrases:

Full text arXiv 1209.1562: pdf, ps.