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arXiv · 1304.2649

σ-Galois theory of linear difference equations

Alexey Ovchinnikov·Michael Wibmer
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Abstract

We develop a Galois theory for systems of linear difference equations with an action of an endomorphism σ. This provides a technique to test whether solutions of such systems satisfy σ-polynomial equations and, if yes, then characterize those. We also show how to apply our work to study isomonodromic difference equations and difference algebraic properties of meromorphic functions.

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Alexey Ovchinnikov, Michael Wibmer. 2013-04-09. σ-Galois theory of linear difference equations. https://doi.org/10.1093/imrn%2Frnu060

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