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arXiv · 2404.10248

All meromorphic solutions of Fermat-type functional equations

Feng Lü
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Abstract

In this paper, by making use of properties of elliptic functions, we describe meromorphic solutions of Fermat-type functional equations $f(z)^{n}+f(L(z))^{m}=1$ over the complex plane $\mathbb{C}$, where $L(z)$ is a nonconstant entire function, $m$ and $n$ are two positive integers. As applications, we also consider meromorphic solutions of Fermat-type difference and $q$-difference equations.

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Feng Lü. 2024-04-16. All meromorphic solutions of Fermat-type functional equations. https://doi.org/10.1017/nmj.2026.10104

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