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arXiv · 1209.1562

On the algebraic independence of generic Painleve transcendents

Joel Nagloo·Anand Pillay
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Abstract

We prove that if y" = f(y,y',t) is a generic Painleve 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 Painleve I equation). For generic Painleve VI we prove a slightly weaker statement.

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BibTeXRIS

Joel Nagloo, Anand Pillay. 2012-09-07. On the algebraic independence of generic Painleve transcendents. https://doi.org/10.1112/s0010437x13007525

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