On the length of binary forms

2010/07/30 by Reznick, Bruce · 2 citations
#11P05 #14N10 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Number Theory (math.NT) #Primary: 11E76

paper · doi:10.48550/arxiv.1007.5485

Abstract

The K-length of a form f in K[x₁,…,x_n], K ⊂ \cc, is the smallest number of d-th powers of linear forms of which f is a K-linear combination. We present many results, old and new, about K-length, mainly in n=2, and often about the length of the same form over different fields. For example, the K-length of 3x⁵ -20x³y²+10xy⁴ is three for K = \qq(√(-1)), four for K = \qq(√(-2)) and five for K = \rr.

Cited by

• The Waring Problem of Complex Binary Forms
• Symmetric tensor decomposition on rational varieties

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