Salem numbers and commensurability classes of arithmetic hyperbolic manifolds

Michelle Chu; Plinio G. P. Murillo

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arXiv · 2506.20552

Salem numbers and commensurability classes of arithmetic hyperbolic manifolds

Michelle Chu·Plinio G. P. Murillo

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Abstract

In this article we show that given a Salem number $\lambda$, a totally real number field $k\subseteq\mathbb{Q}(\lambda+\lambda^{-1})$, and a positive integer $n\geq\mathrm{deg}_k(\lambda)-1$, there exist infinitely many commensurability classes of arithmetic hyperbolic $n$-manifolds defined over $k$ which contain a geodesic of length $\log\lambda$.

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Michelle Chu, Plinio G. P. Murillo. 2025-06-25. Salem numbers and commensurability classes of arithmetic hyperbolic manifolds. https://arxiv.org/abs/2506.20552

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