October 7, 2025Open Access

Unboundedness of shapes of unit lattices in totally real cubic fields

ECEmilio Corso FHFederico Rodriguez Hertz

Key Points

The set of shapes of unit lattices in totally real cubic fields is proven to be unbounded.
This research builds on foundational work by Margulis and Gromov in the study of unit lattices.
The findings indicate implications for the modular surface associated with number fields.
Understanding the shape distribution aids in exploring the geometry of number fields.

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.

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Cite This Study

Corso et al. (Sat,) studied this question.

synapsesocial.com/papers/68e5a0557f330f793683f1b5 https://doi.org/https://doi.org/10.48550/arxiv.2502.16338

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