σ-Galois theory of linear difference equations

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.

References in corpus (5)

• Lax forms of the $q$-Painlevé equations
• Difference independence of the Riemann zeta function
• On sigma-delta-Picard-Vessiot extensions
• Difference integrability conditions for parameterized linear difference and differential equations
• Galois theory of difference equations with periodic parameters

Cited by in corpus (3)

• Hypertranscendence and linear difference equations
• Finiteness properties of affine difference algebraic groups
• Difference modules and difference cohomology