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arXiv · 2110.09466

Geometry-of-numbers methods in the cusp

Arul Shankar·Artane Siad·Ashvin Swaminathan·Ila Varma
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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.

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Arul Shankar, Artane Siad, Ashvin Swaminathan, Ila Varma. 2021-10-18. Geometry-of-numbers methods in the cusp. https://doi.org/10.2140/ant.2025.19.1099

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