On the algebraic independence of generic Painleve transcendents
Algebraic Geometry
2019-02-20 v1 Classical Analysis and ODEs
Logic
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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Cite
@article{arxiv.1209.1562,
title = {On the algebraic independence of generic Painleve transcendents},
author = {Joel Nagloo and Anand Pillay},
journal= {arXiv preprint arXiv:1209.1562},
year = {2019}
}
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11 pages