Geometry-of-numbers methods in the cusp

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 g...

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Bibliographic Details
Published in:arXiv.org 2024-09
Main Authors: Shankar, Arul, Siad, Artane, Swaminathan, Ashvin, Varma, Ila
Format: Article
Language:English
Subjects:
Cusps
Invariants
Operators (mathematics)
Orbits
Polynomials
Representations
Rings (mathematics)
Subgroups
Online Access:Get full text
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Summary: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.
ISSN:2331-8422