## arXiv Analytics

### arXiv:2110.09466 [math.NT]AbstractReferencesReviewsResources

#### Geometry-of-numbers methods in the cusp

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.

On the zeros of certain Poincaré series for $Γ_0^*(2)$ and $Γ_0^*(3)$
On the zeros of Eisenstein series for $Γ_0^* (2)$ and $Γ_0^* (3)$
On the zeros of Eisenstein series for $Γ_0^* (5)$ and $Γ_0^* (7)$