Sums of squares of k-term forms

2024/03/13 by Charu Goel, Goel, Charu, Bruce Reznick +1
Computer Science · Mathematics · #05A10 #05A19 #11B65 #11E25 #11E76 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Graph Labeling and Dimension Problems #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2403.08697

openalex publication_date 2024/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the cones corresponding to sums of squares of n-ary d-ic forms with at most k terms. We show that these are strictly nested as k increases, leading to the usual sum of squares cone. We also discuss the duals of these cones. For n ≥ 3, we construct indefinite irreducible n-ary d-ic forms with exactly k terms for 2 ≤ k ≤ \binomn+d-1n-1.

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