安德烈-丘德诺夫斯基-卡茨的《大意义》
Le théorème d'André-Chudnovsky-Katz « au sens large »
摘要：
西格尔的$E$ -和$G$ -函数被定义为两个在数学上等价的意义，严格和广义。通过采用和完成安德烈的草图，我们陈述并证明了安德烈-丘德诺夫斯基-卡茨定理的广义类比，这是关于广义$G$ -算子（它们是严格意义上抵消$G$ -函数的微分算子）的结构定理。我们由此推出了广义$E$ -算子的一个结构定理，广义$E$ -算子是消去广义$E$ -函数的微分算子.作为这一定理的应用，我们给出了André关于广义$E$ -函数值的代数独立性的Siegel-Shidlovskii定理的一个推广的新证明.
英文摘要：
Siegel's $E$- and $G$-functions were defined in two conjecturally equivalent senses, strict and broad. By taking up and completing a sketch of André, we state and prove the analogue in the broad sense of the André-Chudnovsky-Katz theorem, which is a structure theorem on the $G$-operators in the broad sense (they are differential operators cancelling the $G$-functions in the strict sense). We deduce from that a structure theorem on the $E$-operators in the broad sense, which are differential operators cancelling the $E$-functions in the broad sense. As an application of this last theorem, we give a new proof of a generalization by André of the Siegel-Shidlovskii theorem on the algebraic independence of the values of $E$-functions in the broad sense.
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