$Q$-difference analogue of the Stothers-Mason theorem
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866913166532804608 |
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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 |