English

Solving Order 3 Difference Equations

Rings and Algebras 2025-10-10 v3 Commutative Algebra

Abstract

We classify order 33 linear difference operators over C(x)\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.

Keywords

Cite

@article{arxiv.2402.03868,
  title  = {Solving Order 3 Difference Equations},
  author = {Heba Bou KaedBey and Mark van Hoeij and Man Cheung Tsui},
  journal= {arXiv preprint arXiv:2402.03868},
  year   = {2025}
}

Comments

22 pages, added examples (Section 5.1), removed section 8, moved Mackey's formula to Appendix B, added Appendix C