Algebraic Independence of Painleve First Transcendents

被引：7

作者：

Nishioka, Keiji ^{[1
]}

机构：

[1] Keio Univ, Fac Environm Informat, Fujisawa, Kanagawa 2528520, Japan

来源：

FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA | 2004年 / 47卷 / 02期

关键词：

Painleve first transcendent; Differential automorphism; Irreducibility;

D O I：

10.1619/fesi.47.351

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：351 / 360

页数：10