The Waring Problem of Harmonic Polynomials
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908753843978240 |
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| author | Huang, Hua-Lin Tang, Yilun Ye, Yu Zhu, Rongmin |
| author_facet | Huang, Hua-Lin Tang, Yilun Ye, Yu Zhu, Rongmin |
| contents | This paper investigates the Waring problem of harmonic polynomials. By characterizing the annihilating ideal of a homogeneous harmonic polynomial, i.e., a real binary form that is in the kernel of the Laplacian, we show that its Waring rank equals its degree. Moreover, we show that any linear form can appear in a minimal Waring decomposition of a homogeneous harmonic polynomial, implying that the forbidden locus is empty. We also provide an explicit algorithm for computing the minimal Waring decompositions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_03560 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Waring Problem of Harmonic Polynomials Huang, Hua-Lin Tang, Yilun Ye, Yu Zhu, Rongmin Number Theory Algebraic Geometry Rings and Algebras 11E76, 11P05, 15A06 This paper investigates the Waring problem of harmonic polynomials. By characterizing the annihilating ideal of a homogeneous harmonic polynomial, i.e., a real binary form that is in the kernel of the Laplacian, we show that its Waring rank equals its degree. Moreover, we show that any linear form can appear in a minimal Waring decomposition of a homogeneous harmonic polynomial, implying that the forbidden locus is empty. We also provide an explicit algorithm for computing the minimal Waring decompositions. |
| title | The Waring Problem of Harmonic Polynomials |
| topic | Number Theory Algebraic Geometry Rings and Algebras 11E76, 11P05, 15A06 |
| url | https://arxiv.org/abs/2601.03560 |