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

Wei Chen; Qi Han; Qiong Wang

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

Complex Variables 2021-06-04 v1 Analysis of PDEs

Authors: Wei Chen , Qi Han , Qiong Wang

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.

Keywords

diophantine equations univalent functions special functions

Cite

@article{arxiv.2106.01575,
  title  = {On generalized Fermat Diophantine functional and partial differential equations in $\mathbf{C}^2$},
  author = {Wei Chen and Qi Han and Qiong Wang},
  journal= {arXiv preprint arXiv:2106.01575},
  year   = {2021}
}

Related papers

View all related →