The Waring Problem of Complex Binary Forms

2025/11/18 by Huang, Hua-Lin, Miao, Haoran, Ye, Yu
Computer Science · Mathematics · #11E76 #11P05 #15A06 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #Rings and Algebras (math.RA) #Statistical and numerical algorithms #Tensor decomposition and applications

paper · doi:10.48550/arxiv.2511.14316

openalex publication_date 2025/11/18 · openalex created_date 2025/11/20 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• On the length of binary forms

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