A non-hypergeometric E-function

• 成果类型: Article
• 署名作者: Fresan, Javier; Jossen, Peter
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2021.194.3.7
• 发表日期: 2021
• 页码: 903-942
• 关键词: gevrey series; VALUES

摘要

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 Andre ''s theory of E-operators and Katz's computation of the Galois group of hypergeometric differential equations.