$Q$-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 -weight of zeros, which reduces to the multiplicity of zeros as . Furthermore, we obtain a -difference version of the Stothers-Mason theorem by means of the new definition of the -difference radical, which covers the classical Stothers-Mason theorem as . As applications, we study the polynomial solutions of -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}
}