Submission date: 11 August 2017

Abstract:

We prove that if y&148;=f(y,y',t) is a generic Painlevé equation from the class III and VI, and if y_1,...,y_n are distinct solutions, then y_1,y_1',...,y_n,y_n' are algebraically independent over C(t). This improves the weaker results obtained by the author and Pillay and completely prove the algebraic independence conjecture for the generic Painlevé transcendents.

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

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Full text arXiv 1708.02962: pdf, ps.