On the Waring Problem for Matrices over Finite Fields
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915612445376512 |
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| author | Breaz, Simion |
| author_facet | Breaz, Simion |
| contents | We prove that if $k$ is a positive integer then for every finite field $\mathbb{F}$ of cardinality $q\neq 2$ and for every positive integer $n$ such that $q^n>(k-1)^4$, every $n\times n$ matrix over $\mathbb{F}$ can be expressed as a sum of three $k$-th powers. Moreover, if $n\geq 7$ and $k<q$, every $n\times n$ matrix over $\mathbb{F}$ can be written as a sum of two $k$-th powers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_11805 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Waring Problem for Matrices over Finite Fields Breaz, Simion Rings and Algebras Commutative Algebra We prove that if $k$ is a positive integer then for every finite field $\mathbb{F}$ of cardinality $q\neq 2$ and for every positive integer $n$ such that $q^n>(k-1)^4$, every $n\times n$ matrix over $\mathbb{F}$ can be expressed as a sum of three $k$-th powers. Moreover, if $n\geq 7$ and $k<q$, every $n\times n$ matrix over $\mathbb{F}$ can be written as a sum of two $k$-th powers. |
| title | On the Waring Problem for Matrices over Finite Fields |
| topic | Rings and Algebras Commutative Algebra |
| url | https://arxiv.org/abs/2505.11805 |