English

$Q$-difference analogue of the Stothers-Mason theorem

Number Theory 2026-05-28 v1 Complex Variables

Abstract

In this paper, we give a new definition of the qq-weight of zeros, which reduces to the multiplicity of zeros as q1q\to 1. Furthermore, we obtain a qq-difference version of the Stothers-Mason theorem by means of the new definition of the qq-difference radical, which covers the classical Stothers-Mason theorem as q1q\to 1. As applications, we study the polynomial solutions of qq-difference Fermat type functional equations.

Keywords

Cite

@article{arxiv.2605.27876,
  title  = {$Q$-difference analogue of the Stothers-Mason theorem},
  author = {Jian-Tang Lu and Xing-Xing Lu and Zhi-Tao Wen},
  journal= {arXiv preprint arXiv:2605.27876},
  year   = {2026}
}