Unboundedness of shapes of unit lattices in totally real cubic fields

2025/02/22 by Corso, Emilio, Hertz, Federico Rodriguez · 2 citations
#Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2502.16338

Abstract

The question of the distribution of shapes of unit lattices in number fields, pioneered by Margulis and Gromov, has lately attracted considerable interest, not least because of the lack of available results. Here we prove that the set of shapes of orders of totally real cubic fields is unbounded in the modular surface.

Cited by

• Classification of totally real number fields via their zeta function, regulator, and log unit lattice
• Unit lattices of D₄-quartic number fields with signature (2,1)

Related

• The shapes of pure cubic fields
• Shapes of unit lattices in D_p-number fields
• Lower order terms in the shape of cubic fields
• Most totally real fields do not have universal forms or Northcott property
• A space of weight one modular forms attached to totally real cubic number fields