A non-hypergeometric E-function

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...

Full description

Saved in:
Bibliographic Details
Published in:Annals of mathematics 2021-11, Vol.194 (3), p.903-942, Article 903
Main Authors: Fresán, Javier, Jossen, Peter
Format: Article
Language:English
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0003-486X
1939-8980
DOI:10.4007/annals.2021.194.3.7