On Siegel's problem for \(E\)-functions

DOI10.4171/RSMUP/107MaRDI QIDQ2697595

Tanguy Rivoal, Stéphane Fischler

Publication date: 12 April 2023

Published in: Rendiconti del Seminario Matematico della Università di Padova (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.06817

zbMATH Keywords

hypergeometric seriesasymptotic expansionsSiegel's \(E\)- and \(G\)-functions

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Transcendence theory of other special functions (11J91) Generalized hypergeometric series, ({}_pF_q) (33C20)

Related Items (2)

A note on $G$-operators of order $2$ ⋮ D-finiteness, rationality, and height. III: Multivariate Pólya-Carlson dichotomy

Cites Work

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• On the structure of the set of \(E\)-functions satisfying linear differential equations of second order
• On the values of \(G\)-functions
• Nilpotent connections and the monodromy theorem: Applications of a result of Turrittin
• On the algebraic dependence ofE-functions
• A NOTE ON THE ASYMPTOTIC EXPANSION OF GENERALIZED HYPERGEOMETRIC FUNCTIONS
• Differential equations associated with nonarithmetic Fuchsian groups
• An example of an arithmetic Fuchsian group.
• Differential Operators with Nilpotent p-Curvature
• Transcendental Numbers. (AM-16)
• Some finite summation theorems and an asymptotic expansion for the generalized hypergeometric series

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