论文标题
$ e $ functions的lindemann-weierstrass定理
A Lindemann-Weierstrass theorem for $E$-functions
论文作者
论文摘要
Siegel在1929年引入了$ e $ - 功能，以概括指数函数的Diophantine特性。在Shidlovskii，Nesterenko和André的Siegel方法的发展之后，Beukers在2006年证明了$ e $ dunctions的代数独立性的最佳结果，从而推广了Lindemann-weiersstrass theorem。从那时起，似乎没有关于单个$ e $ unction的值之间关系的一般结果。我们证明，安德烈（André）的$ e $ operators和beuker的结果使Lindemann-Weierstrass定理以$ e $ functions的线性独立性配方进行。结果，我们表明，整个超几何函数的代数参数上的所有先验值在$ \ overline {\ mathbb {q}} $上都是线性独立的。
$E$-functions were introduced by Siegel in 1929 to generalize Diophantine properties of the exponential function. After developments of Siegel's methods by Shidlovskii, Nesterenko and André, Beukers proved in 2006 an optimal result on the algebraic independence of the values of $E$-functions which generalizes the Lindemann-Weierstrass theorem. Since then, it seems that no general result was stated concerning the relations between the values of a single $E$-function. We prove that André's theory of $E$-operators and Beuker's result lead to a Lindemann-Weierstrass theorem for $E$-functions in its linear independence formulation. As a consequence, we show that all transcendental values at algebraic arguments of an entire hypergeometric function are linearly independent over $\overline{\mathbb{Q}}$.
