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arXiv · 2605.27876

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

Jian-Tang Lu·Xing-Xing Lu·Zhi-Tao Wen
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Abstract

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

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Jian-Tang Lu, Xing-Xing Lu, Zhi-Tao Wen. 2026-05-27. $Q$-difference analogue of the Stothers-Mason theorem. https://arxiv.org/abs/2605.27876

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