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arXiv · 2402.07481

On Salem numbers which are exceptional units II

Toufik Zaimi
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Abstract

We show that for any natural number $n$ satisfying $n\equiv 4 \mod 8$ and $n\not\equiv 0 \mod 5$, and for any odd integer $t\geq \frac{n+6}{2}$ there are infinitely many Salem numbers ${\alpha}$ of degree $2t$ such that ${\alpha}^n-1$ is a unit. This result, obtained using a generalization of a construction due to Gross and McMullen [5], partially completes the main result of [7].

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Toufik Zaimi. 2024-02-12. On Salem numbers which are exceptional units II. https://arxiv.org/abs/2402.07481

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