Solving Order 3 Difference Equations

2024/02/06 by Heba Bou KaedBey, Mark van Hoeij, KaedBey, Heba Bou +3
Computer Science · Mathematics · #12H10 #39A06 #Advanced Algebra and Logic #Commutative Algebra (math.AC) #FOS: Mathematics #Polynomial and algebraic computation #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2402.03868

openalex publication_date 2024/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We classify order 3 linear difference operators over ℂ(x) that are solvable in terms of lower order difference operators. To prove this result, we introduce the notion of absolute irreducibility for difference modules, and classify (for arbitrary order) modules that are irreducible but not absolutely irreducible.

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