English

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.

Keywords

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}
}
R2 v1 2026-06-22T01:28:03.581Z