Solving Order 3 Difference Equations

• DOI: 10.48550/arxiv.2402.03868
• Publication Date: 2024-01-01
• Authors: Heba Bou KaedBey; Mark van Hoeij; Man Cheung Tsui
• Keywords: Rings and Algebras (math.RA); FOS: Mathematics; Mathematics - Rings and Algebras; Mathematics - Commutative Algebra; Commutative Algebra (math.AC); 12H10, 39A06

22 pages, added examples (Section 5.1), removed section 8, moved Mackey's formula to Appendix B, added Appendix C<br/>We classify order $3$ linear difference operators over $\mathbb{C}(x)$ 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.<br/>