A non-hypergeometric E-function

Javier Fresàn*, Peter Jossen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

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

Original languageEnglish
Pages (from-to)903-942
Number of pages40
JournalANNALS OF MATHEMATICS
Volume194
Issue number3
DOIs
Publication statusPublished - Nov 2021

Keywords

  • Differential galois theory
  • E-function
  • Fourier-laplace transform
  • Hypergeometric series

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