Metadata only
Datum
2021-11Typ
- Journal Article
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 Andre ''s theory of E-operators and Katz's computation of the Galois group of hypergeometric differential equations. Mehr anzeigen
Publikationsstatus
publishedExterne Links
Zeitschrift / Serie
Annals of MathematicsBand
Seiten / Artikelnummer
Verlag
Princeton University PressThema
E-function; Differential Galois theory; Fourier-Laplace transform; hypergeometric seriesOrganisationseinheit
09532 - Jossen, Peter Simon (ehemalig) / Jossen, Peter Simon (former)