On the height of polynomials that split completely over a fixed number field
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911155638763520 |
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| author | Tromp, Thian |
| author_facet | Tromp, Thian |
| contents | Let $K/\mathbb{Q}$ be a finite extension. We prove that the minimal height of polynomials of degree $n$ of which all roots are in $K^\times$ increases exponentially in $n$. We determine the implied constant exactly for totally real $K$ and $K$ equal to $\mathbb{Q}(\sqrt{-1})$ or $\mathbb{Q}(\sqrt{-3})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_12064 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the height of polynomials that split completely over a fixed number field Tromp, Thian Number Theory Let $K/\mathbb{Q}$ be a finite extension. We prove that the minimal height of polynomials of degree $n$ of which all roots are in $K^\times$ increases exponentially in $n$. We determine the implied constant exactly for totally real $K$ and $K$ equal to $\mathbb{Q}(\sqrt{-1})$ or $\mathbb{Q}(\sqrt{-3})$. |
| title | On the height of polynomials that split completely over a fixed number field |
| topic | Number Theory |
| url | https://arxiv.org/abs/2509.12064 |