arXiv Open Access 2020

Counting Salem numbers of arithmetic hyperbolic 3-orbifolds

Mikhail Belolipetsky Matilde Lalín Plinio G. P. Murillo Lola Thompson

Lihat Sumber

Abstrak

It is known that the lengths of closed geodesics of an arithmetic hyperbolic orbifold are related to Salem numbers. We initiate a quantitative study of this phenomenon. We show that any non-compact arithmetic $3$-dimensional orbifold defines $c Q^{1/2} + O(Q^{1/4})$ square-rootable Salem numbers of degree $4$ which are less than or equal to $Q$. This quantity can be compared to the total number of such Salem numbers, which is shown to be asymptotic to $\frac{4}{3}Q^{3/2}+O(Q)$. Assuming the gap conjecture of Marklof, we can extend these results to compact arithmetic $3$-orbifolds. As an application, we obtain lower bounds for the strong exponential growth of mean multiplicities in the geodesic spectrum of non-compact even dimensional arithmetic orbifolds. Previously, such lower bounds had only been obtained in dimensions $2$ and $3$.

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Penulis (4)

Mikhail Belolipetsky

Matilde Lalín

Plinio G. P. Murillo

Lola Thompson

Format Sitasi

APA MLA BibTeX

Belolipetsky, M., Lalín, M., Murillo, P.G.P., Thompson, L. (2020). Counting Salem numbers of arithmetic hyperbolic 3-orbifolds. https://arxiv.org/abs/2001.07851

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Informasi Jurnal

Tahun Terbit: 2020
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓