Monogenic Strictly-Perron Polynomials
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916918447833088 |
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| author | Jones, Lenny |
| author_facet | Jones, Lenny |
| contents | A monic polynomial $f(x)\in {\mathbb Z}[x]$ of degree $n$ is called monogenic if $f(x)$ is irreducible over ${\mathbb Q}$ and $\{1,θ,θ^2,\ldots ,θ^{n-1}\}$ is a basis for the ring of integers of ${\mathbb Q}(θ)$, where $f(θ)=0$. A strictly-Perron polynomial is the minimal polynomial of a Perron number $λ$ such that $λ$ is neither a Pisot number, an anti-Pisot number, nor a Salem number. For any natural number $n\ge 2$, we prove that there exist infinitely many monogenic strictly-Perron polynomials of degree $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_18946 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Monogenic Strictly-Perron Polynomials Jones, Lenny Number Theory A monic polynomial $f(x)\in {\mathbb Z}[x]$ of degree $n$ is called monogenic if $f(x)$ is irreducible over ${\mathbb Q}$ and $\{1,θ,θ^2,\ldots ,θ^{n-1}\}$ is a basis for the ring of integers of ${\mathbb Q}(θ)$, where $f(θ)=0$. A strictly-Perron polynomial is the minimal polynomial of a Perron number $λ$ such that $λ$ is neither a Pisot number, an anti-Pisot number, nor a Salem number. For any natural number $n\ge 2$, we prove that there exist infinitely many monogenic strictly-Perron polynomials of degree $n$. |
| title | Monogenic Strictly-Perron Polynomials |
| topic | Number Theory |
| url | https://arxiv.org/abs/2508.18946 |