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arXiv · 2106.01575

On generalized Fermat Diophantine functional and partial differential equations in $\mathbf{C}^2$

Wei Chen·Qi Han·Qiong Wang
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Abstract

In this paper, we characterize meromorphic solutions $f(z_1,z_2),g(z_1,z_2)$ to the generalized Fermat Diophantine functional equations $h(z_1,z_2)f^m+k(z_1,z_2)g^n=1$ in $\mathbf{C}^2$ for integers $m,n\geq2$ and nonzero meromorphic functions $h(z_1,z_2),k(z_1,z_2)$ in $\mathbf{C}^2$. Meromorphic solutions to associated partial differential equations are also studied.

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Wei Chen, Qi Han, Qiong Wang. 2021-06-03. On generalized Fermat Diophantine functional and partial differential equations in $\mathbf{C}^2$. https://arxiv.org/abs/2106.01575

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