Algebraic Independence of Painlevé First Transcendents
Algebraic Independence of Painlevé First Transcendents
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Painlevé 第一超越数的代数独立性
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
K. Nishioka
中科院分区：
文献类型：
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作者：
K. Nishioka
利用其不可约性，证明了复系数有理函数域上的Painleve一阶超越及其一阶导数在代数上是独立的。一个特例表明，由Painleve一次超越生成的微分场的微分自同构群是平凡的。
It will be proved that Painleve first transcendents and their first derivatives are algebraically independent over the rational function field with complex coefficients, by the use of the irreducibility. A particular case indicates that the group of differential automorphisms of the differential field generated by a Painleve first transcendent over the rational function field is trivial.