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PreprintarXiv licencearXiv

Entire solutions of higher order Briot-Bouquet equations

  • Alexandre Eremenko
  • Tuen Wai Ng
  • Teng Zhang
Open at sourcePDFDOICite

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.

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Cite

BibTeXRIS
BibTeX
@misc{eremenko2026entire,
  title = {{Entire solutions of higher order Briot-Bouquet equations}},
  author = {Alexandre Eremenko and Tuen Wai Ng and Teng Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.20438},
  eprint = {2610.20438},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.20438},
}
RIS
TY  - UNPB
TI  - Entire solutions of higher order Briot-Bouquet equations
AU  - Alexandre Eremenko
AU  - Tuen Wai Ng
AU  - Teng Zhang
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.20438
UR  - https://arxiv.org/abs/2610.20438
AB  - 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.
ER  -