5 citations · 5 across the 3 of their papers we have counts for
8 papers
Spherical Heron triangles and elliptic curves
Tinghao Huang, Matilde Lalín, Olivier Mila
We define spherical Heron triangles (spherical triangles with "rational" side-lengths and angles) and parametrize them via rational points of certain families of elliptic curves. W…
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…
Non-commensurable hyperbolic manifolds with the same trace ring
Olivier Mila
We prove that there are infinitely many pairwise non-commensurable hyperbolic -manifolds that have the same ambient group and trace ring, for any . The manifolds can b…
The trace field of hyperbolic gluings
Olivier Mila
We determine the adjoint trace field of gluings of general hyperbolic manifolds. This provides a new method to prove the nonarithmeticity of gluings, which can be applied to the cl…
Hyperbolic manifolds and pseudo-arithmeticity
Vincent Emery, Olivier Mila
We introduce and motivate a notion of pseudo-arithmeticity, which possibly applies to all lattices in with . We further show that under an additional assump…
Nonarithmetic hyperbolic manifolds and trace rings
Olivier Mila
We give a sufficient condition on the hyperplanes used in the inbreeding construction of Belolipetsky-Thomson to obtain nonarithmetic manifolds. We construct explicitly infinitely…
Symmetries of weight enumerators and applications to Reed-Muller codes
Martino Borello, Olivier Mila
Gleason's 1970 theorem on weight enumerators of self-dual codes has played a crucial role for research in coding theory during the last four decades. Plenty of generalizations have…
On the Stabilizer of Weight Enumerators of Linear Codes
Martino Borello, Olivier Mila
This paper investigates the relation between linear codes and the stabilizer in of their weight enumerators. We prove a result on the finiteness of stabili…