All meromorphic solutions of Fermat-type functional equations
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914418074320896 |
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| author | Lü, Feng |
| author_facet | Lü, Feng |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10248 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | All meromorphic solutions of Fermat-type functional equations Lü, Feng Complex Variables 30D30 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. |
| title | All meromorphic solutions of Fermat-type functional equations |
| topic | Complex Variables 30D30 |
| url | https://arxiv.org/abs/2404.10248 |