4 papers
Hyperbolic Heron Triangles and Elliptic Curves
Matilde Lalín, Olivier Mila
We define hyperbolic Heron triangles (hyperbolic triangles with "rational" side-lengths and area) and parametrize them in two ways as rational points of certain elliptic curves. We…
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…
Regulator proofs for Boyd's identities on genus 2 curves
Matilde Lalín, Gang Wu
We use the elliptic regulator to recover some identities between Mahler measures involving certain families of genus 2 curves that were conjectured by Boyd and proven by Bertin and…
Mahler Measure and the Vol-Det Conjecture
Abhijit Champanerkar, Ilya Kofman, Matilde Lalín
The Vol-Det Conjecture relates the volume and the determinant of a hyperbolic alternating link in . We use exact computations of Mahler measures of two-variable polynomials to…