Sums of squares of k-term forms
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911796225376256 |
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| author | Goel, Charu Reznick, Bruce |
| author_facet | Goel, Charu Reznick, Bruce |
| contents | 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 $n \ge 3$, we construct indefinite irreducible $n$-ary $d$-ic forms with exactly $k$ terms for $2 \le k \le \binom{n+d-1}{n-1}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_08697 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sums of squares of k-term forms Goel, Charu Reznick, Bruce Number Theory 11E76, 11E25, 05A19, 05A10, 11B65 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 $n \ge 3$, we construct indefinite irreducible $n$-ary $d$-ic forms with exactly $k$ terms for $2 \le k \le \binom{n+d-1}{n-1}$. |
| title | Sums of squares of k-term forms |
| topic | Number Theory 11E76, 11E25, 05A19, 05A10, 11B65 |
| url | https://arxiv.org/abs/2403.08697 |