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arXiv · 2205.10601

Orbits in Lattices

Matthew Dawes
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Abstract

We exhibit algorithms for calculating Tits' buildings and orbits of vectors in a lattice $L$ for certain subgroups of $\operatorname{O}(L)$. We discuss how these algorithms can be applied to understand the configuration of boundary components in the Baily-Borel compactification of orthogonal modular varieties and to improve the performance of computer arithmetic of orthogonal modular forms.

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Matthew Dawes. 2022-05-21. Orbits in Lattices. https://doi.org/10.1016/j.jnt.2024.06.013

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