English

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}
}