Counting lattice points in central simple algebras with a given characteristic polynomial
Number Theory
2025-03-05 v1
Abstract
We extend the asymptotic formula for counting integral matrices with a given irreducible characteristic polynomial by Eskin, Mozes and Shah in 1996 to the case of counting elements in a maximal order of certain central simple algebra with a given irreducible characteristic polynomial.
Keywords
Cite
@article{arxiv.2503.02371,
title = {Counting lattice points in central simple algebras with a given characteristic polynomial},
author = {Jiaqi Xie},
journal= {arXiv preprint arXiv:2503.02371},
year = {2025}
}