7 citations · 7 across the 8 of their papers we have counts for
10 papers
On Salem numbers of degree 4 and arithmetic hyperbolic orbifolds
Cayo Dória, Plinio G. P. Murillo
In this article, we construct an arithmetic hyperbolic orbifold such that, any square-rootable Salem number of degree at most over is realized as…
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…
Counting Salem numbers arising from arithmetic hyperbolic orbifolds
Michelle Chu, Plinio G. P. Murillo, Otto Romero +1
The relationship between Salem numbers and short geodesics has been fruitful in quantitative studies of arithmetic hyperbolic orbifolds, particularly in dimensions 2 and 3. In this…
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…
Hyperbolic manifolds with a large number of systoles
Cayo Dória, Emanoel M. S. Freire, Plinio G. P. Murillo
In this article, for any we construct a sequence of compact hyperbolic -manifolds with number of systoles at least as $\mathrm{vol}(M_i)^{1+\frac{1}{3n(n+1)}…
Hyperbolic 3-manifolds with large kissing number
Cayo Dória, Plinio G. P. Murillo
In this article we construct a sequence of non compact finite volume hyperbolic -manifolds whose kissing number grows at least as …
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…
On the systole growth in congruence quaternionic hyperbolic manifolds
Vincent Emery, Inkang Kim, Plinio G. P. Murillo
We provide an explicit lower bound for the sytole in principal congruence covers of compact quaternionic hyperbolic manifolds. We also prove the optimality of this lower bound.
Systole of congruence coverings of arithmetic hyperbolic manifolds
Plinio G. P. Murillo
In this paper we prove that, for any arithmetic hyperbolic -manifold of the first type, the systole of most of the principal congruence coverings satisfy $$sys_{1}(M…
On growth of systole along congruence coverings of Hilbert modular varieties
Plinio G. P. Murillo
We study how the systole of principal congruence coverings of a Hilbert modular variety grows when the degree of the covering goes to infinity. We prove that given a Hilbert modula…