A non-hypergeometric E-function
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Date
2021-11
Publication Type
Journal Article
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yes
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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.
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published
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Journal / series
Volume
194 (3)
Pages / Article No.
903 - 942
Publisher
Princeton University Press
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Edition / version
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Subject
E-function; Differential Galois theory; Fourier-Laplace transform; hypergeometric series
Organisational unit
09532 - Jossen, Peter Simon (ehemalig) / Jossen, Peter Simon (former)