Hypertranscendance des systèmes aux différences diagonaux
Hypertranscendance des systèmes aux différences diagonaux
复制标题
对角差异系统的超超越
作者：
C. Hardouin
本文讨论了对角差分方程组解的导数代数独立的判别准则。其关键思想在于从微分算子和差分算子的交换性中推导出原始差分模块的一系列迭代扩展，从而将问题置于差分伽罗瓦理论的框架中，并最终将其简化为线性代数中有关椭圆曲线或环面的因子组的练习。
Abstract This paper deals with criteria of algebraic independence for the derivatives of solutions of diagonal difference systems. The key idea consists in deriving from the commutativity of the differentiation and difference operators a sequence of iterated extensions of the original difference module, thereby setting the problem in the framework of difference Galois theory and finally reducing it to an exercise in linear algebra on the group of divisors of the involved elliptic curve or torus.