论文标题
非冬季电子功能
A non-hypergeometric E-function
论文作者
论文摘要
我们在否定的西格尔（Siegel）的问题中回答所有电子函数是否是超小节电子功能中的多项式表达式。也就是说，我们表明，如果三个订单的不可还原差分运算符在超几何类别中歼灭了电子功能，则其傅立叶变换的奇异性受到限制以满足一般不存在的对称属性。证明依赖于安德烈的电子运营商理论以及Katz对高几何微分方程的Galois组计算。
We answer in the negative Siegel's question whether all E-functions are polynomial expressions in hypergeometric E-functions. Namely, we show that if an irreducible differential operator of order three annihilates an E-function in the hypergeometric class, then the singularities of its Fourier transform are constrained to satisfy a symmetry property that generically does not hold. The proof relies on André's theory of E-operators and Katz's computation of the Galois group of hypergeometric differential equations.
