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

Fuente: arXiv
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Main Authors: Lu, Jian-Tang, Lu, Xing-Xing, Wen, Zhi-Tao
Format: Preprint
Published: 2026
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author Lu, Jian-Tang
Lu, Xing-Xing
Wen, Zhi-Tao
author_facet Lu, Jian-Tang
Lu, Xing-Xing
Wen, Zhi-Tao
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2605_27876
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle $Q$-difference analogue of the Stothers-Mason theorem
Lu, Jian-Tang
Lu, Xing-Xing
Wen, Zhi-Tao
Number Theory
Complex Variables
39B32, 30D35
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.
title $Q$-difference analogue of the Stothers-Mason theorem
topic Number Theory
Complex Variables
39B32, 30D35
url https://arxiv.org/abs/2605.27876