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arXiv · 1309.4025

On stable lattices and the diagonal group

Uri Shapira·Barak Weiss
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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.

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Uri Shapira, Barak Weiss. 2013-09-16. On stable lattices and the diagonal group. https://arxiv.org/abs/1309.4025

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