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arXiv:2110.09466 [math.NT]AbstractReferencesReviewsResources

Geometry-of-numbers methods in the cusp

Arul Shankar, Artane Siad, Ashvin Swaminathan, Ila Varma

Published 2021-10-18, updated 2022-06-22Version 2

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.

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