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arXiv · 2601.03560

The Waring Problem of Harmonic Polynomials

Hua-Lin Huang·Yilun Tang·Yu Ye·Rongmin Zhu
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Abstract

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.

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Hua-Lin Huang, Yilun Tang, Yu Ye, Rongmin Zhu. 2026-01-07. The Waring Problem of Harmonic Polynomials. https://arxiv.org/abs/2601.03560

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