paper

Solving Order 3 Difference Equations

arXiv:2402.03868 · doi:10.1016/j.jsc.2025.102419

Abstract

We classify order linear difference operators over 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.

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

Solving Order 3 Difference Equations · wovepaper