Geometry-of-numbers methods in the cusp
Number Theory
2025-05-21 v3 Representation Theory
Abstract
In this article, we develop new methods for counting integral orbits having bounded invariants that lie inside the cusps of fundamental domains for coregular representations. We illustrate these methods for a representation of cardinal interest in number theory, namely that of the split orthogonal group acting on the space of quadratic forms.
Cite
@article{arxiv.2110.09466,
title = {Geometry-of-numbers methods in the cusp},
author = {Arul Shankar and Artane Siad and Ashvin Swaminathan and Ila Varma},
journal= {arXiv preprint arXiv:2110.09466},
year = {2025}
}
Comments
40 pages