On stable lattices and the diagonal group
Dynamical Systems
2013-09-17 v1 Number Theory
Abstract
Inspired by work of McMullen, we show that any orbit for the action of the diagonal group on the space of lattices, accumulates on a stable lattice. We use this to settle a conjecture of Ramharter about Mordell's constant, get new proofs of Minkowski's conjecture in dimensions up to seven, and answer a question of Harder on the volume of stable lattices.
Cite
@article{arxiv.1309.4025,
title = {On stable lattices and the diagonal group},
author = {Uri Shapira and Barak Weiss},
journal= {arXiv preprint arXiv:1309.4025},
year = {2013}
}