The Waring Problem of Complex Binary Forms
Number Theory
2025-12-01 v1 Algebraic Geometry
Rings and Algebras
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.
Keywords
Cite
@article{arxiv.2511.14316,
title = {The Waring Problem of Complex Binary Forms},
author = {Hua-Lin Huang and Haoran Miao and Yu Ye},
journal= {arXiv preprint arXiv:2511.14316},
year = {2025}
}