The Waring Problem of Complex Binary Forms
Fuente:
arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917109791981568 |
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| author | Huang, Hua-Lin Miao, Haoran Ye, Yu |
| author_facet | Huang, Hua-Lin Miao, Haoran Ye, Yu |
| contents | The Waring problem of forms concerns the expression of homogeneous multivariate polynomials as sums of powers of linear forms. This paper focuses on complex binary forms, and we solve the Waring problem for them using basic tools in algebra and analysis. In particular, we present elementary treatments of the Apolarity Lemma and Sylvester's 1851 Theorem, which are easily accessible and will provide an ideal approach for future extension to the general case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_14316 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Waring Problem of Complex Binary Forms Huang, Hua-Lin Miao, Haoran Ye, Yu Number Theory Algebraic Geometry Rings and Algebras 11E76, 11P05, 15A06 The Waring problem of forms concerns the expression of homogeneous multivariate polynomials as sums of powers of linear forms. This paper focuses on complex binary forms, and we solve the Waring problem for them using basic tools in algebra and analysis. In particular, we present elementary treatments of the Apolarity Lemma and Sylvester's 1851 Theorem, which are easily accessible and will provide an ideal approach for future extension to the general case. |
| title | The Waring Problem of Complex Binary Forms |
| topic | Number Theory Algebraic Geometry Rings and Algebras 11E76, 11P05, 15A06 |
| url | https://arxiv.org/abs/2511.14316 |