Linear independence of powers for polynomials
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866908448849920000 |
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| author | Crăciun, Alexandru |
| author_facet | Crăciun, Alexandru |
| contents | Given $k \ge 2$ polynomials in $d \ge 1$ variables with coefficients in a field of characteristic $0$, such that no two are linearly dependent, we show that for any integer $r$ greater than $\max\left\{k {k-1 \choose 2}, 2\right\}$, the $r$-th powers of the polynomials are linearly independent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_10163 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Linear independence of powers for polynomials Crăciun, Alexandru Commutative Algebra 12E05 Given $k \ge 2$ polynomials in $d \ge 1$ variables with coefficients in a field of characteristic $0$, such that no two are linearly dependent, we show that for any integer $r$ greater than $\max\left\{k {k-1 \choose 2}, 2\right\}$, the $r$-th powers of the polynomials are linearly independent. |
| title | Linear independence of powers for polynomials |
| topic | Commutative Algebra 12E05 |
| url | https://arxiv.org/abs/2507.10163 |