2205.00041
Hyperexponential solutions of elliptic difference equations
Thierry Combot
correctmedium confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper proves and algorithmically realizes bases for rational, pseudo-rational, and hyperexponential solutions of elliptic difference equations with non‑torsion shift (Theorem 1), built on a universal divisor, pseudo‑rational building blocks Θ, and a δ‑principality filter for hyperexponentials. The candidate solution restates the same core ideas in difference‑field/Riemann–Roch language. Aside from minor overclaims (e.g., that each jump pattern yields at most one K‑line), the model’s reasoning aligns closely with the paper’s construction and proofs.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The work correctly generalizes Petkovšek-type methods to elliptic curves by introducing a universal divisor, Θ-factors, and a δ-principality filter for hyperexponential solutions, with proofs of termination and completeness. The central arguments are sound and well-motivated. Minor clarifications on constants/scalars and a few implementation details would improve readability and reproducibility.