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math.GT2025
On Systole, Kissing Number and Volume of Arithmetic Manifolds
Plinio Guillel Pino Murillo
The purpose of this expository article is to give a down-to-hearth introduction to the notion of an arithmetic group and arithmetic manifold. To achieve this we have decided to bri…
math.GT2025
Salem numbers and commensurability classes of arithmetic hyperbolic manifolds
Michelle Chu, Plinio G. P. Murillo
In this article we show that given a Salem number , a totally real number field , and a positive integer , there exist…
math.GT2020
Counting Salem numbers of arithmetic hyperbolic 3-orbifolds
Mikhail Belolipetsky, Matilde Lalín, Plinio G. P. Murillo +1
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 tha…