Polynomials whose nth powers have prescribed multiple-of-nth-degree coefficients
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912403702153216 |
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| author | Yelton, Jeffrey |
| author_facet | Yelton, Jeffrey |
| contents | We show under a mild hypothesis that given field elements $a_0, \dots, a_m \in K$, there always exists a degree-$m$ polynomial whose $n$th power whose degree-$jn$ coefficient is equal to $a_j$ for $0 \leq j \leq m$. We provide an alternate proof for the $n = 2$ case which is more constructive. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_24013 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Polynomials whose nth powers have prescribed multiple-of-nth-degree coefficients Yelton, Jeffrey Number Theory Algebraic Geometry 12E05, 14E20 We show under a mild hypothesis that given field elements $a_0, \dots, a_m \in K$, there always exists a degree-$m$ polynomial whose $n$th power whose degree-$jn$ coefficient is equal to $a_j$ for $0 \leq j \leq m$. We provide an alternate proof for the $n = 2$ case which is more constructive. |
| title | Polynomials whose nth powers have prescribed multiple-of-nth-degree coefficients |
| topic | Number Theory Algebraic Geometry 12E05, 14E20 |
| url | https://arxiv.org/abs/2505.24013 |