Multiplicity and vanishing lemmas for differential and \(q\)-difference equations in the Siegel-Shidlovsky theory

DOI10.1007/s10958-012-0652-3zbMath1418.39007OpenAlexW2073318948WikidataQ125052621 ScholiaQ125052621MaRDI QIDQ2256728

Daniel Bertrand

Publication date: 20 February 2015

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-012-0652-3

zbMATH Keywords

functional equationsSiegel's theoremDeligne's irregular Hodge theorySiegel-Shidlovsky theorem

Mathematics Subject Classification ID

Hodge theory in global analysis (58A14) Difference equations, scaling ((q)-differences) (39A13) Transcendental methods, Hodge theory (algebro-geometric aspects) (14C30)

Related Items (1)

A note on meromorphic solutions of linear partial differential equations of second order

Cites Work

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• An effective version of the Lindemann-Weierstrass theorem for interpolation determinants
• An analogue of Shidlovskii's lemma for certain \(q\)-difference equations
• Arithmetic theory of \(q\)-difference equations. The \(q\)-analogue of Grothendieck-Katz's conjecture on \(p\)-curvatures
• Gevrey series of arithmetic type. I: Purity and duality theorems
• A refined version of the Siegel-Shidlovskii theorem
• On Siegel–Shidlovskii's theory for q-difference equations
• On applications of diophantine approximations
• Galois theory of fuchsian q-difference equations
• Interpolation on algebraic groups

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