English

On Fermat Diophantine functional equations and little Picard theorem

Classical Analysis and ODEs 2019-12-24 v3

Abstract

We discuss equivalence conditions on the non-existence of non-trivial meromorphic solution to the Fermat Diophantine equations fm(z)+gn(z)=1f^m(z)+g^n(z)=1 with integers m,n2m,n\geq2, from which other approaches to prove little Picard theorem are provided.

Keywords

Cite

@article{arxiv.1711.04924,
  title  = {On Fermat Diophantine functional equations and little Picard theorem},
  author = {Jingbo Liu and Qi Han and Wei Chen},
  journal= {arXiv preprint arXiv:1711.04924},
  year   = {2019}
}