2013/09/16 by Uri Shapira, Shapira, Uri, Barak Weiss +1 · 1 citation
Mathematics · #22F30 #37A17 #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT) #math.DS #math.NT #msc:22F30 #msc:37A17
paper · pdf · doi:10.48550/arxiv.1309.4025
arxiv created 2013/09/16 · arxiv updated 2013/09/17
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.