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arXiv · 2104.06290

Fermat functional equations over Riemann surfaces

Xianjing Dong·Liangwen Liao·Kai Liu
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Abstract

We investigate the existence of non-trivial holomorphic and meromorphic solutions of Fermat functional equations over an open Riemann surface $S$. When $S$ is hyperbolic, we prove that any $k$-term Fermat functional equation always exists non-trivial holomorphic and meromorphic solution. When $S$ is a general open Riemann surface, we prove that every non-trivial holomorphic or meromorphic solution satisfies a growth condition, provided that the power exponents of the equations are bigger than some certain positive integers.

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Xianjing Dong, Liangwen Liao, Kai Liu. 2021-04-13. Fermat functional equations over Riemann surfaces. https://arxiv.org/abs/2104.06290

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