Year: 2026
Type: preprint
Abstract: For a meromorphic function $f$ in the complex plane, we determine when $f$ and $f^{(k)}$ are algebraically dependent. This happens precisely when $f$ belongs to the class $W$ of elliptic functions and their degenerates, or satisfies a linear differential equation $f^{(k)} + af + b = 0$ with constant coefficients. The case of functions having a pole was settled previously. We complete the proof by treating entire solutions.
Source: arXiv (Cornell University)
Authors: Eremenko, Alexandre, Ng, Tuen Wai, Zhang, Teng
Institution: Purdue University West Lafayette
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221927987