The Waring Problem of Harmonic Polynomials
Number Theory
2026-01-09 v1 Algebraic Geometry
Rings and Algebras
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.
Cite
@article{arxiv.2601.03560,
title = {The Waring Problem of Harmonic Polynomials},
author = {Hua-Lin Huang and Yilun Tang and Yu Ye and Rongmin Zhu},
journal= {arXiv preprint arXiv:2601.03560},
year = {2026}
}